I'd venture a guess to say that they lied about making the moons disappear too. No proof to say that they didn't make them go poof for awhile, but there's no proof to say that they did other than their word and that could easily be seen as an opportunist political ploy to influence the Khajjiit.
They only claim to have made them reappear, though I personally think they were responsible for making them disappear in the first place. If not them, who? I think we can safely rule out the other Tamrielic powers (since it'd've been counter-productive), leaving the Sload, Maomer, and Akaviri as possible candidates, but the Sload and Maomer, if they had such power, would be the greater threat to the Thalmor, and so they'd have attacked them instead. I'll still admit that it could very well have been any of the Akiviri races.
This makes it pretty obvious that after their initial success, their main objective (and with it one could only assume the vast majority of their military endeavors) was focused on Cyrodiil and toppling the Empire. To just say "Oh it was just their force in Cyrodiil" to me is a major understatement. The annihilation of their forces (and it makes the distinction, they were completely and utterly destroyed unlike the ones in Hammerfell) in Cyrodiil logically implies the annihilation of their main field army and thus would (To me) be a military blunder on behalf of the Dominion. It was after that, that the Dominion began to search for a peace option. These series of events make me think that their losses in Cyrodiil were enough to make the Dominion rethink their position, and weakened their military position enough that they were afraid of behind over run. Their goals turned from what they asked for in the ultimatum to the destruction of the Empire, only for their luck to be turned on them and place them in a position of dire peril, one that forced them to make peace at the risk of further Imperial counter attacks. Its speculated that the Empire, had they continued to push, could have at least pushed the Dominion off continental Tamriel, and its my belief they shared the same fears.
Titus Mede II was actually the one to sue for peace, though the Dominion's acceptance of said peace after just losing a major piece of territory does show weakness on their part. They no longer thought it was worth wile to wage an offensive war deep in enemy territory.
Without a doubt, the Red Ring was a blunder, and a major defeat, however the question is how much damage did it actually deal? I find it unlikely that they posted the majority of their armies directly around the Imperial City, where the battle took place. The Thalmor had to have soldiers garrisoning the rest of Cyrodiil, fighting resistance groups inside of Cyrodiil, fighting the Hammerfell Front, and on home guard duty. It was likely their largest single gathering of soldiers, and a major section of their military, but I think it'd be infeasible to have more than half of their army stationed there. Now, I definitely agree with the idea that, had the Thalmor not surrendered, they still would have had to withdraw the remainder of their forces from Cyrodiil, be it immediately or after a period of fierce fighting. They had just had their main force destroyed, and the legions that achieved that would likely be more than capable of bringing the same fate to the smaller remnant forces in Cyrodiil. But the Thalmor's peaceful withdrawal was actually advantageous for them. It prevented them from losing the forces they had occupying the other cities of Cyrodiil, unlike the natives, who had their garrisons killed when the cities were taken.
No question the war severely hindered the Empire. I believe I read that the Imperial Legions were based somewhere along those of the Roman Republic, so the destruction of three legions is about 18,000 men (If thats the right conclusion, which I'm not certain it is) however I don't believe that the Empire had a mere three legions to its service. It says no other legion had more than half strength, so we don't how many more legions are available for Cyrodiil but we also don't know how many men make an Aldmeri Army, it could be more or less, but in any situation we know it was enough to force the Dominion to the peace table.
The numbers are definitely going to be uncertain, but I think the 6,000 men / legion count should be fair.
Now regrading the Thalmors occupation in Hammerfell, the occupiers were in a hostile land were forced to keep vast supply line, and in the case of the Dominion they have one hell of a sea lane to upkeep with no land route to bring in supplies, men and money. From the sounds of it, they had little or no local populace to help fill their ranks and it would be extremely difficult to fill their dwindling ranks in Hammerfell and means they would have to constantly send more troops from Summerset or Valenwood (which Valenwood's not fully on board with the Thalmor anyway, just like before) to resupply and reinforce when every Raga available seemed to be fighting to expel the invaders. At that, the Raga are masters of guerrilla warfare, something I doubt the Altmer were really equipped to deal with effectively. Were not talking about a well established presence with military instillation and great defensible hardpoints like the French had in Vietnam, which had been gradually becoming apart of the French Empire since 1859 up until 1955. That gave France close to 96 years to dig in and fortify their strength where as the Thalmor faced constant unified resistance with no friendly backing and no real time to establish themselves. That said, to me it sounds like it was far to costly to keep and hold their new found holdings for it to really be worth it to the Thalmor who only held their ground for a few years.
What part of their supply line was vast? Summerset & Valenwood are quite close to Southern Hammerfell, whose cities are all coastal. Assuming that "Southern Hammerfell" means the four southern cities of Hammerfell, the Ragada only had one free port of their own. I think it's safe to assume the Altmer were more than capable of taking on the Sentinel fleet + any imperial privateers there may have been. Also, what makes you think the Raga are masters of guerrilla warfare? I thought they left that to the Argonians, while they busied themselves with nuclear swords. Is this just something I missed out on, having never played Redguard?
Otherwise, I think your assessment is fair. They would be under attack from all sides, at all times. The natives would mostly be uncooperative (though there were some exceptions, i.e. that girl in whiterun), and they wouldn't be able to really fortify themselves. It'd be expensive, and continued occupation obviously wasn't worth it for them. The question is, during the occupation, did they give worse than they got? I'd say yes. Southern Hammerfel is in shambles. When they took that territory, it was from the cold, dead hands of brave patriots. When they lost it, it was given up by a tired army of people who probably just wanted to go home.
For recovery times, I've always been under the impression that the Altmer genetically could not produce as fast as man nor in the numbers of man as a trade off for their extravagantly long life spans. No expert on population here, but wouldn't the same thing apply for man as well? who already has an advantage on population regrowth? in any case I don't believe the Thalmor would repopulate faster than the Cyrodiil, just my own personal opinion though.
As far as I know, the only source that explains merish infertility claims that elven reproduction is tied to population pressure, and so elves cannot reproduce when populations are high / stable, but after taking a hit they can bounce right back. So, the rates of repopulation should be about the same. I'd say that men should have a bit of an edge just because the lack of regulation / state family planning probably makes... ahem... acts of breeding more common among man than mer. However, the Thalmor likely did more population damage during the war, so men have a longer way to recover.
Like I said, as the Empires borders shrink so does the Thalmors ability to influence those regions. The idea of getting the Empire to ban Talos was to get them to enforce it was it not? That's something they cannot do if their falling apart and more and more regions begin to fall out of the Imperial sphere of influence. If the Dominion is content to just let men kill each other that's all honky dory, but its not hurting Talos worship as much as its emboldening it as reason to stand up against the Thalmor pawns. To me, this just doesn't sound like a great victory to me and I'm not quite dazzled by the Thalmor as everyone else seems to be. Just my opinion on the matter.
Well, the Empire's borders might not be shrinking. In my playthrough, the Stormcloak Rebellion was really just a purge of all those devout enough to fight for their beliefs, and an excuse to rile up the survivors against Talos worship (think anti-Islamic sentiment). But even if the Stormcloaks win, having your advantage shrink doesn't actually hurt you, it just doesn't help as much.
As for the dazzling, I'll admit that I'm prejudiced for them, partially just because I like to play Altmer characters (given a choice, I always play the wizard), but I think that you may have the wrong impression about the forums at large. The only other person who I know for sure to be a fan of the Thalmor is AE ALTADOON. Most everyone else seems to be either on your side (Huleed, Haute) or neutral / not invested (Lady N, a thousand others). It's possible that things are different in the Fan Fiction section, or in GD, but around here I think you're among supporters.