Ok well it sounds like the shop you have your car at has no idea what they are talking about. If they said one cylinder leaks, so what.
Did they tell you y? I could leak for a multitude of reasons. Valve stuck open, valve is burnt, bad rings, ect. Or it could be a crack in the block. But that is less likley. Get them to tell you why you need a new engine not that you just need a new one.
You can put a 1G motor in your car. Many people have done it. You will pass emissions if the engine is tuned and running properly.
Y do you want a JDM motor? What is the purpose of spending all that extra money?
If you do this all right and find the stuff you need at a resonable price i imagine that you could do it all within 3000.
Good luck