Then it won't work. Mid engine would be FWD moved to the back, Rear Engine is Porsche/VW or nothing honestly.
Your design plan would completely ignore the idea that the oil would be starving every single time you hit the gas, and not to mention the problems of the entire gearbox running in reverse.
There's a LARGE number of reasons that people rarely build rear engine vehicles, custom or otherwise. Even though it lends well to acceleration and off the line power, rear engine vehicles tend to be tricky to put around a turn. And as you can see here there's very limited options outside of the companies who actually make rear engine cars, unless you're willing to build your own transaxle, or make one fit.
As my dad, and most people in real life, or even on this forum will probably tell you after this ordeal:
If you're not sure what you're doing, you probably shouldn't be doing it.