I thought the rules were different for postseason vs. regular season. I believe in regular season a TD on the opening possession still ends the game. I also believe that a regular season game cannot go past the end of the 5th quarter (and 5th quarter is 10 minutes long.)

All of the above would imply an advantage to taking the ball first in regular season OT.

That implies that the odds of the other team scoring on a standard drive is higher than ~43% (43% = 49% chance of 2pt success - 6% chance of missing the XP).

That strikes me as high in the aggregate. Perhaps scores are more likely in OT when defenses are tired?

and then whatever the losing coach chose was obviously the wrong decision.

Assuming Team A gets the ball first, and Team b second...

If the game goes to a 3rd possession, and assuming each team has a 40% chance of scoring and ending the game on a given drive (as a thought exercise... roll with it), then the chances of winning on a given drive are as follows:

3rd possession, Team A wins .4 (or game continues .6)
4th, B, .24 (which is .6*.4)
5th, A, .144
6th, B, .0864
7th, A, .05184
8th, B, .031104

Keep going far enough and sum each teams win probabilities on each of their possible drives (the sum of odd numbered drives for team A and the sum of even numbered drives for Team B), and you get 62.4% odds for Team A to win the game, or 37.6% for Team B to win the game.

Adjusting the assumed chance of scoring on a given drive, win probability changes as follows:

.25 chance of scoring on a given drive: A wins the game 55.5% of the time, B wins 44.5% of the time
.28, A wins 57%, B wins 43%
.3, A wins 58%, B wins 42%
.35, A wins 60.2%, B wins 39.8%
.4, A wins 62.4%, B wins 37.6%
.45, A wins 64.4%, B wins 35.6%

I think based on this and the assumption that the probability of scoring on a given drive is greater than .28, as the coach of Team B I would take my 43% chance of winning by going for 2 after scoring a TD on the 2nd possession rather than keep playing.

at least for playoffs. Both pro and college football have evolved to the point where offense has a big advantage. Giving both teams a possession, perhaps with only 2-point tries on TDs, should resolve a winner in an efficient time frame that will replicate the natural way the game is played instead of a contrived shootout that is unnecessary.

It seems that in general college offenses are less efficient than NFL (with the caveat that so are the defenses) which means an "extra innings" approach would be less likely to result in a quick resolution to the game. Thoughts?

higher than NFL. Not sure that answers your question, but I would guess either the NFL or college football would resolve a winner in a fairly similar amount of time (and quantity of plays), with college perhaps being done even faster. I would add the must go for 2-points on a TD (less than 50% conversation) to expedite a final result quicker in the two TDs on first possession scenario.

the easiest one I can think of is to move field position from the 25 to midfield.

Is that it eliminates two very important variables from consideration: field position and the game clock. It also eliminates special teams from consideration as well, with the exception of the PAT/FG unit.

but with the playoff games taking over the sport, would 1 guaranteed possession under normal football rules extend the game a significant number of plays on average, with only 2-point tries on TDs, and if tied after 1 possession each, next score wins? Shootouts are tolerable in the regular season, but I would prefer the new NFL style OT in the playoffs. You have a better sense of just how big of an issue number of plays is for college age athletes, but unless that is a compelling case, use the NFL rules.

I admit to being a fogey and think tie games are OK The best OTs in sports are those which stay closest to normal rules. Baseball. Basketball, playoff hockey, and golf are good in that regard. Tennis and FB less so

Your idea of moving the ball back rewards god defenses. I hate OT field goals on an initial 4th and 15

Made OT special in playoffs

I agree with the rest of your post, too

At least have to make a 1st down or 2 to kick a FG

As a HS wrestler before reg season OT, I had 2 ties: 1 vs a very good wrestler. 1 vs a poor one
1 got me a big pat on the back & the other almost cost me my starting spot