I would say it should not be a problem. Set it in the hole complete, put it on some blocks to get the hight ya want and roll the car forward or back as needed. Then build some mounts. The good thing abot a 30s car is the rails are straight.
First thing I'd do is get the measurements of the engine that is or supposed to be in the car and then go search for sizes of engines I was interested in using. I take it that you have a 300 on hand and that is why you want to use it. If so, bust out the tape measure for what you want to put in and where you want it to go. Keep in mind things like engine/trans mount location. Think about possible firewall modifications and what kind of steering setups you have or want. Lots of things to think about.
how bout a slant six? check out the slant six forums they make some good power http://www.slantsix.org/
Ever thought of 'building' the stock mill? it would mean some fabricating of bits but souping an engine is simply a matter of following a well trodden path. I hope you are upgrading the brakes etc too? 1930's Mopars weren't known for their great brakes.
A guy in my car club put a GMC 292 in a 32 Buick coupe. The 292 developed "issues", so he dropped in a 350 he had laying around. He said that he was surprised the 350 was an easier swap. I think a bent 8 in a car like that just isn't right, just pointing out that life is full of surprises. Bill