As someone with experience in the epic build and also familiar with Crosleys (thought I was going to die in one), my opinion is that you don't have enough time.
The Crosley was a turd when it was new, and the stock now rusty chassis is beyond redemption even for slow IOE material. Newly rebuilt Crosley brakes on a hill are responsible for my second scariest vehicle experience (after nailing a tree with a formula car). So going with what is under that lunchbox of a car is, in my opinion, out of the question.
So it's a shell on something else. The problem is the Crosley is really really tiny and stupidly narrow. So any OEM type chassis that you could want is going to be wide enough to make it look borderline-stupid, and have a wheelbase that is much too long. The labor involved in chopping up a mini-truck chassis to make it fit, or just making your own ladder frame that ties a set of miata crossmembers together is going to be about the same.
The real time disappears into everything else. The sheet metal, the pedal assembly, new floors, the steering, wiring, where the hell do I put a gas tank, ducting the radiator, scrounging yards, and on and on and on.
I'm the last guy to want to discourage such a build, but I gave myself 7 months of almost every weekend. I got laid off 2 weeks ahead of BFE and spend every waking moment (with help!) working on the car. It still wasn't done. There was easily another 12 hours of 8 or so skilled heroes thrashing on the damn thing at the track after I became a zombie.
3 months isn't enough, no matter how you decide to do it. So go ahead, just don't start using anything stronger than caffeine.
Edit: sorry for the longwinded $.02, I just developed a bit of a twitch when I read "3 months"
Brrrrrrrrrrrrrrrrrrr.