Okay, I apologise one final time for the rather large detour this thread has now taken, but I'm sure we can be done with this soon.

Thank you all for your comments, anyway.
Let us decide what is most important to achieve in case it is impossible to satisfy every need.
This approach is best.
Firstly, the key thing is to
have a month of Morning Star at all. Secondly, we want the number of the month to correspond to its number of days, so that scripts like Cyrano's can function properly. Thirdly, we want the name of the month to correspond to its index number (according to Morrowind, not it's actual place in the order) and day number, so that 'annual events' and the journal can function properly.
In an incremental order, these desires correspond to the options we've been shown. Hrnchamd's initial solution covered the first objective. Cyrano's solution then covered both the first and the second objectives. Mine then covered the first, second and third. There was, however, one problem with mine, which was that the year would turn over at the wrong time. This brings us to the fourth objective, that the year turns over correctly.
The first objective is rather simple: it's been achieved by all the patches so far. The second is just a matter of ensuring that the correct days number is assigned to the correct month index number. Very simple. The third is again just a matter of ensuring the correct string variable is applied to the appropriate days number and month index number. Very simple. These can be achieved with little to no effort at all.
The fourth objective is similarly simple. I think it is relatively obvious to presume that the year number turns over each time the month index number list reaches its end. In Hrnchamd's first solution, then, the year progressed when Evening Star (Month 11) changed into Morning Star (Month 0). In Cyrano's solution, the year progressed when Evening Star (Month 12) changed into Morning Star (Month 1). So clearly there is no fixed turnover point.
So, in order to get everything working in a simple manner, I present to you one last grid of excellentness:
Month # of Days # of Days Name Name (Beth) (MCP) (Beth) (MCP) 0 N/A 31 N/A Morning Star 1 31 31 Sun's Dawn Sun's Dawn 2 28 28 First Seed First Seed 3 31 31 Rain's Hand Rain's Hand 4 30 30 Second Seed Second Seed 5 31 31 Mid Year Mid Year 6 30 30 Sun's Height Sun's Height 7 31 31 Last Seed Last Seed 8 31 31 Heartfire Heartfire 9 30 30 Frostfall Frostfall 10 31 31 Sun's Dusk Sun's Dusk 11 30 30 Evening Star Evening Star
The new month of Morning Star has been added. Objective 1 is fulfilled.
All the vanilla Bethesda months remain unchanged. No scripts or events can be affected. So that is perfect, exactly as we want, fulfilling objectives 2 and 3.
The year, presuming it worked in Hrnchamd's first patch, will turn over at the end of Evening Star. Objective 4 is fulfilled. Everything is perfect!
Except! Damn, I have just realised exactly what everyone else may have been saying (though never explicitly, which isn't very helpful

). Which is that in the truest 'lore' sense, the entire original Morrowind calendar was broken. Because Sun's Dawn (the second month, February) should have 28 days, not First Seed. So in the absolutely truest sense of 'lore', the number of days should be shifted up one place on the grid each, with Morning Star's 31 then being cycled round to the end to Evening Star.
How
ever, in this way, by following in the absolutely strictest sense of lore (and ignoring the fact that Morrowind itself screwed this up entirely), we break the rather important objective 2. Ultimately, it comes down to how imperative it is that Cyrano's scripts function as they do (personally, I've always used the GameHour variable to see how many days have changed, not the Day variable itself), and whether there are any other scripts that rely on knowing the number of days in a given month (I personally cannot think of any).
If it is imperative these scripts function, we use my grid above. If it is not imperative, we shift the number of days up by one place each, giving an entirely lore correct calendar that is able to still run yearly events, have 12 months, and turn the year over correctly (objectives 1, 3 and 4). (EDIT:Oh, just checked and that was the original fix: oh dear!

)
Phew. I think that covers everything. I apologise again for any distraction I have caused.