You really need Cartest v4.5. It doesn't have the Spyder in the built-in database, but if you have the relevant specs you can create a new car (or easier, duplicate an older MR-2 and modify so it looks like the spyder).
http://www.cartestsoftware.com/cartest4.5/index.html
This program is actually a little "too" powerful for your simple comparison, but once you get the details worked out it is a fantastic tool for doing hypothetical "what-if" comparisons. I use it a few times a year.
Short answer is - tire size changes like FD changes don't actually change acceleration times much unless there is a change in necessary gear changes to achive the target speed. Think about it this way - with shorter gearing, you get better acceleration in low gears, but you spend less time there before a taller and slower gear is needed.
IMO, for autocross, it comes down to minimizing required 2-3 shifts. 59 MPH sounds about right. 55 Mph would get annoying. On track, in most situations, gearing should be selected to be at redline in top gear on the fastest straight. But don't listen to me, what do I know?

Anyone recommend a good text for gearing issues? I have a stack of books that I haven't even read...
_________________
Mike Whitney
whit32@gmail.com, 919-454-5445
V10, V8, V8t, I6, I6, V6, F4t, I4, I4, I4, I4, I2, 1, 1