I recently swapped out the 305 fuel injected engine for a 350 crate engine. ever since the engine swap the car stays running with the key in the off position, a few seconds later it decides to finally shut off. does anyone have an idea of what may be wrong?

 

This is only a guess, but sounds like you've got ignition power going to something other than the direct ignition switch source. Or, something is backfeeding the ignition power.

What that is - no clue.

Did you stay with fuel injection, or convert it over to carb?