$4k left for an LS swap......
Good luck!! You must be doing all the work yourself then. But seriously, as you said,
"tight!" Bout time you buy the engine and all the required stuff, such as headers, adapter plates, ECU flashing, tranny, tranny tunnel modification, etc., you are already past the $4k mark.
You might want to rethink this before getting to deep into the project and wishing you hadn't or realizing you're in over your head.
But, it sounds like a great project and will be very fun to do and drive. Just make sure you have all you ducks in a row and everything is well planned and thought out.