Hi Steve! I own an MR2 also and that thought has also crossed my mind a lot.
I can toss you more material to read up than you'd honestly know what to deal with- EV potential is staggering- but unless you've found some pretty mad Brushless DC motor (EV Smart Zytek motor?) or you've found a real monster of a Brushed forklift motor for drag racing i'd go AC and leave DC in the dirt. It's nothing against DC- the simplicity can be awesome- but AC intrinsically is more efficient and can do regenerative breaking without some of the wacky measures DC has to pull. As for using a Model 3's batteries- they're not much taller than the gas tank, so honestly I'd be more concerned about the front striking the steering shaft or pushing too far back into the engine bay. There was also a strut in the rear to add more support where the floor pan merges into the engine bay that you'd have to cut out and work around- I remember it VERY well when I redid my entire fuel system.
That Tesla3 drivetrain is interesting, and would easily plop into the back of an AW11.
It'll happen soon, but not yet. The Model 3's motor is Synchronous-Reluctance AC instead of the S/X which is Internal Permanent Magnet; SynR has a computer that switches on/off electromagnets in tune with the motor instead of using rare-earths that are constantly "on" to be far cheaper and be much more efficient. The tradeoff is they need powerful computers to control them, and so far we don't have a controller yet. The GOOD news however, is the Leaf's AC motor is capable of 300HP natively, is well packaged with it's inverter (so making a cooling circuit is easy) and are very cheap.
As for putting an Electric into a classic car? Definitely, it just depends entirely on what it is and why. For some it's an interesting idea to get a chassis back onto the road- for others, it's because their parts scarcity is so bad it's legit one of the only ways to keep it on the road (See the EV Ferrari 308 story; that happened because it's 3 motors and custom adapter plate to the transaxle was comparable in cost to a new engine). It also really is just what "complements" the vehicle more.
Also, there's reasons to keep the (Manual) transmissions. Hard to do any kind of regen on a box that isn't straight-cut gears, but torque multiplication is a thing and DC motors have a 'range' they like to be at where they're the most efficient. There's a few DC Motor swapped muscle cars I can post that use the 2-speed lenco box that is pneumatically-driven to keep torque in the 600lb/ft range.
In reply to 03Panther :
All electric motors are extremely inefficient at turning electricity into movement.
(This has since been answered, sorry-GQ) If a motor is rated for 90% efficiency that means 90% of all energy that enters it is converted from electrical energy to mechanical energy, compared to even the best gas motors barely breaking 40%. Now, if you got into the nitty-gritty of TYPES of motors, there are plenty you'd never want in a car but not exactly for those reasons.
The Model 3's Motor is somewhere in the 92-95% efficiency range, but they are ballpark estimates based on what we can back-engineer and from outside experts like Sandy Munroe. Of course, that efficiency is it spinning in a bench; I think the total car's efficiency (energy to get it down the road) is something above 80% still.