Here's how I considered those issues before/during watching them in this order. Somehow your numbers got messed up, but your concerns are there.
- the stardates are not in sync with either broadcast nor production orders. Wild swings.
- Most are grouped in the middle of the stardates for TOS season 3
TOS stardates are mixed between seasons also, and surprisingly some episodes fit well when mixed.
- TAS episode Stardates of 1254.4, 3138.3 and 7403.6 are "out there". Also, that's a span of 6.15 years (assuming 1000 stardates equal one solar year.)
I consider 1254 and 7403 to be possible errors. 3183 mixes that episode in with the first and second seasons. 1312 to 6770 is still a little more than 5 years, though. However, 5 years might not be an exact mission length (give or take some travel time in explored space, for example), or, since the last few in stardate order have plots that deal heavily with diplomacy, it is possible that a fan theory I tend to reject, which is that there were a few small missions after the big 5 year mission was over, could be employed in this case.
- I like to explain the physical changes of the sets like in engineering plus the second door on the bridge would come and go when combined with TOS.
Not a great fix here, but I overlook some conflicted elements from within TOS itself when viewed in stardate order (color of Spock's scanner, nylon vs velour uniforms, etc.).
You pointed out to me that the actual Engine Room set change does not conflict in production date, air date, or stardate orders. "The Practical Joker" would fall between the last appearance of Engineering in its Season 1 configuration and the first appearance it in its Season 2 configuration; the TAS version would thus have to be another version of the room somewhere else--not ideal but I could accept it.
The door on the bridge is problem, but maybe the wall in front of it retractable in some way? (Khan does say he had sealed of the exit routes (plural) in Space Seed, and Kirk runs right to the panel where the door would be and starts working controls.)
- Two of the TAS stardates are 4 or less stardates (~one day) between episodes.
I can't dispute that. TOS itself includes this phenomenon. When making my list I went with the assumption that even though stardates were in a set order, warping great distances could still slow the reported units down; other episodes benefit from being closely spaced.
- Mudd's Passion is bumping up to the two months (164 stardates) needed for The Paradise Syndrome. Plus more time would be needed to tow and repair the ship.
I saw "Mudd's Passion" being after the Paradise Syndrome to fit well. The ship had been mostly repaired but they still had to get some more supplies at a mining planet where they also were expected to apprehend criminal Harry Mudd. Next is "The Enterprise Incident" in which Kirk says they were "due for an overhaul two months ago." That works so well it almost seems like it's on purpose. The
Enterprise has been fixed just well enough to stay in service, but not put back to tip-top shape before sending her where she might be captured by Romulans. Why give them a nicer target than you must?
Those are just a few of my thoughts. Thanks for sharing yours.