[Tom Kirkham]

2.88 has a unique carrier.
3.07 to 3.73 and (4.10) take the low case.
3.91 and bigger take the high case.

But a 2.88 will work with a five speed until you can find a different carrier.
Note: the total first gear multiplication on a stock 427 AC Shelby Cobra is 3.54 (stock diff ratio) * 2.32 (1st gear, close ratio toploader) = 5.86
Now your set up would be 2.88 * 2.87 = 8.27
as you can see 8.27 is a lot more total gear reduction than 5.86 which is about the lower limit and not burn up clutches.

Hope this helps