If that's an older 700R4 I would consider trading it for a rebuilt one with a torque converter to match your new engine and rear end. However the 700R4's can be a little expensive. Another option might be to run what you got until it goes away (and you are saving for its replacement).

For the rear end I would probably buy a new limited slip differential case and a 3.42:1 to 3.72:1 ring and pinion, put it back together with new bearings and seals.

If you do all the tear out/installation work yourself you might squeek by with $6k total. You can add bling to it later to save some money .........

Kitz