And with the Coyote motor you still have the powder metal rods and hyperpathetic pistons. So it's still a time bomb. How low is your mileage? I put a blower on my stock motor at around 60K and it was healthy. I put about 5K on it and the motor blew three pistons getting on the freeway one day going to work. And I wasn't even in boost. That was about 12psi and a very conservative tune.
You can probably find a blower kit and shortblock for less then 8K. But that's not what kills your budget. It's all the little things like needing a bigger MAF, bigger fuel system, etc. Then finding out your current clutch doesn't like the power level and lets go.
As for the transmission, what are your plans for the car? I ran a 3650 for a long time with a motor making around 550rwhp. But it never saw the track and I didn't do high rpm clutch dumps. I have a T-56 now, but that's mostly because I found a screaming deal on it.
No matter how conservative the tune is, I think 12psi it too high for the stock short block