Maybe I'm missing something here, but...
Have you looked into splitting your arrangements? Use points for one night, or two (and buy the tickets required)...and then pay cash for the remaining 2 or 3 nights? (Maybe staying someplace where you're not required to buy park tickets since you're not planning to do the parks all 4 days?)
As for renting...it's not that hard, and your 37 points makes it pretty low risk...even if you get unlucky enough to be one of the miniscule few for whom it doesn't work (like me--I got scammed -- my "sad story" is in one of Doc's stickies on the R/T Board), you're not only risking "only" 37 points/$370 (or so), but also you're really not risking much of anything since your current plans give you choices that are only $2 different!
So it seems to me your risk of renting is actually getting $370 (or so) vs not...might take some of the angst out of it to think of it that way...
But I'm really curious to see if the idea of using points for just one or two nights, to use up your 37 points that will expire, and doing the rest of your trip on cash, might be a viable solution?
Good luck...