The reason TesTool is crashing is because you have too many mods loaded. Apparently you only have one too many mods loaded if only disabling UL makes it work, but this is a common issue with TesTool. It just can't handle too many mods at once. There's no reason you need to merge UL though, since most of the objects added are unique rather than altered existing ones.
When you climb into the Bag of Holding to return to your former location, everything is supposed to fade to black, then fade back in at your destination. Normally this works fine. But twice now (which amounts to maybe 10% of the times I've tried it) the view remained black and didn't fade back in. The first time this happened, I tried teleporting to different places using Intervention spells and another teleport ring I had, but the view remained black at each place. Then, I tried going back to Tel Uvirith using that ring, and the view cleared up. The game proceeded normally from there.
The second time it happened, I tried using the Tel Uvirith ring right away, and the game crashed.
I'll have a look at the scripts, but I think it's bound to be a little buggy because the fix is kind of a cludge to get around the 72 hour bug. The only real way to fix it is to make an MWSE version. I intend to make an MWSE add-on at some point, which includes the Bag of Holding as well as a new script for the alchemy sorter that will sort all ingredients type objects so it can include all modded ingredients, removing the necessity for the SriKandy add-on if you're using the MWSE patch.
In the readme, you mention that if you're already Archmagister when you load up Uvirith's Legacy, that you can still get his key off his disgruntled apprentice. However, I killed Gothren a while before joining the Telvanni to become the hortator for the main quest. I loaded this mod just before joining the Telvanni so I was clearly not the Archmagister beforehand, yet Gothren was dead. Anyway, after my stronghold, advanced to Archmagister, and being prompted to get the seal and then stumbling around Gothren's tower for a while, I read the readme and, having given the disgruntled apprentice his promotion and thus having him leave, I loaded an earlier save when he was still around. However, after exhausting any options that came to mind to coax the key away from him (talking, killing and searching his person) I am still keyless.
Tl;dr - Any possibility that playing through House Telvanni with Uvirith's Legacy installed but Gothren dead before installation would be causing my key deprivation? Or am I foolishly overlooking something obvious?
You should have been able to get the key the very first time you talked to Gothren's apprentice, regardless of what you've done prior. If you don't have it, you can add it in via. console. It should be AddItem->key_Arch_Gothren 1. I'll look at his dialogue, because he should have given it to you in his first greeting if you didn't have it in your inventory already.
Which console commands would I need to use to activate all the teleports in the different towers? I don't feel like doing that all over again for every update.
The platforms are activated via. journal entry. If you type in Journal UV_FyrDoor 50, and so on for all the towers, they should all be activated.