Buy a pair of decent 2-ton (or higher) jack stands & a small rolling floor jack. Sam's Club sometimes sells a kit for under $100, but shop around.
Get a few short chains from a pawn shop or 2nd-hand store. If you can't find any, just buy some 1/4" chain & threaded links form a hardware store. I'd get a 3' section & maybe a shorter one. Use them to hook onto the exhaust manifolds to lift the engine/trans like this. Use a decent ratchet strap to control the tilt.
Since you're obviously not rushing, get EVERYTHING disconnected & drained before you rent the hoist. That way, you can be sure to return it the same day. If you can get the replacement engine & trans ready beforehand, you might even be able to reinstall them at the same time if you rent it on Fri & return it on Mon. If you've done this before & have all the tools, it's possible to do it in one day.
Then you can take your time reconnecting everything.