A couple of other ideas (recognizing this is a '54 Ford):
1) Mount the motor on the rear carrier, no driveshaft or slip joint, still need a coupler if you don't use a chain or belt drive, or
2) Put an IRS in the back (many hotrodders, nowadays, known as "restomodders", do anyway, which again eliminates the slip joint, needs a coupler and an arbitrarily long driveshaft. Unlike the old days where Corvette and Jag were the only readily available choices, there are a few more out there for IRS these days.
One other issue you need to think about with your industrial motor (seems to be a secret of what it is with the way you took the pics, so I have to guess that's what it might be given the keyed shaft) is cooling.
Most stationary motors have an integral fan on the rotor, which is completely useless at low RPM, and that's where most people dump the highest current into a traction motor. You can get some motors that have a separately motored fan from things like machine tools (not cheap).
Maybe you have that taken care of, but getting gobs of air down a trans tunnel that's plugged by a motor is a tough nut to crack as well. Especially fun when you have a block of batteries blocking airflow to the tunnel.
You also are starting out with a heavy car. Coupling it to the rear end by whatever means only gives you a 3:1 to 5:1 torque increase. If you're using a 3600 RPM motor, you don't have much choice but to couple to the rear end if you want to have a chance at hitting highway speeds, If it fits in a tunnel, with direct drive acceleration could be sucky, though.
I'm sure you've done the math on wheel speed. Less likely you did the math for acceleration. Putting the motor anywhere, including the engine bay, needs thinking about cooling and not merely about how to attach the rotor to a prop shaft.
As I said, maybe you've thought about all this, but if you (or future project folks) haven't, you may be in for a nasty & expensive surprise.