I'm fine with about a 33" tire. That is what I have on there now.
I am guessing that by the time you put this truck together even if you went out of your way to keep it as low as possible, the newly built truck would probably be similar to your current truck on 37's as far as height.
I am not trying to discourage anybody from building this - I think it would be an awesome machine, it just is gonna ride like **** and be tall.