Posting this here for posterity: since I'll probably have to buy a 6MT pumpkin for whatever diff anyways, I've been researching my rear-end ratio options and trying to rationalize the differences on-track between the options. (Keep in mind the 7AT's transmission ratios are substantially different than 6MT...).
Stock 7AT is 3.357, Stock 6MT is 3.692, and there's also a 4.08 available that people have done. I'm estimating my tires at 789 revs-per-mile for 275/35R18 (although it will vary by tire options of course), and the 7AT's first 5 gears are 4.924, 3.194, 2.043, 1.412, 1.000 - I hope to rarely ever use 6, and never 7, as they get weaker up there. I guess we can pretty much ignore first gear too, I can't imagine needing it on any track.
Redline speeds in gears 2-5:
3.357: 52, 82, 118, 167 (current)
3.692: 47, 74, 107, 152
4.080: 43, 67, 97, 137
Thinking about straight lengths and speeds at my most-typical local tracks: generally I'm in 3 and 4 almost exclusively right now with only the big straight at TWS requiring a move to 5th. My end-speed on that straight is ~135 now on a good lap, but that might get higher as I learn to exit onto it faster, and it's almost certainly a bit higher in the less-common CW direction, so probably plan on 150 as a soft "top speed" that I'll rarely exceed anywhere (and if I do, it won't be for long or matter much). On most of the more-typical straights (e.g. back straight of MSR-H, back straight of TWS), on a good lap I'm sometimes bumping the redline in 4th right at the end, so ~115-120, but it's not worth upshifting before turn-in currently (but I might have to if I get faster eventually). Only COTA has really required 2nd gear, and I won't hit that often.
4.08 seems like it's not a good option right off the bat. I'd be using up a substantial portion of 5th gear on a regular basis (multiple times per lap typically), and I'd be shifting to 6th halfway down the big straight at TWS going CW eventually. I'm not sure I trust the strength of 6 or 7 on this trans to be in them hard every lap on my closest course
3.692 is a little bit of a wash with stock on shift points, maybe slightly better. I'd definitely be able to carry through some corners staying in 4th where I currently have to drop to 3rd to keep revs up, and that's worth a lot. However, straights that I can currently stay in 4th through (TWS back, MSR back) would now definitely require a 4->5 upshift partway down the straight. 5th should last me all the way to the end of the big TWS straight.
I used to think the universal "Lower is better" argument for rear-end ratios only really applied to drag racing, but I finally managed to convince myself it's true in the general case for road-racing as well (ignoring shift-points above). What it boils down to is this: the lower the rear end ratio, the shorter each transmission gear's speed range gets. The shorter the transmission gears get, the more time you spend higher in the power band (given equivalent shifting strategies using both rear ends). So, I think I'll take the stock 6MT ratio when I switch diffs.