We have a fold up cherry picker and it's great. In my opinion for what you're trying to do and on a budget I see them for sale frequently on Craigslist and Offerup for very reasonable prices or for trade. I think a 1000 lb. lift would work just fine. Just make sure you're on good concrete and take things slow.
I think Tubman is right, my 1 ton chain hoist is wore out. I bought it off of FB market place used. Is very handy to have around, but with a flathead & transmission it just spins around like a stripped gear or something. Will lift just the engine fine though.
I see the engine cranes on marketplace all the time pretty cheap.
The wife engine blew up 2 weeks ago and been searching for the used crane and nothing available. Story of my life

My plan is to buy the crane this month and next month a engine.
If nothing shows up by the end of the month, will go to harbor freight and buy the 1 ton crane. Just call it a day.
Thats why am working on the 8BA now. Next month will need the engine stand for the wife engine. Trying to get it disassembled and put away. Figure out what it needs to put it back together and later this winter work on it some more.
The crank cleaned up easily. I spent yesterday with gasoline, wire brushes, scotchbrite, vacuum cleaner, compressed air .... I believe with more cleaning, the rotating assembly can be used as is. For a good running used engine.
I set the crank back in and installed the timing gear, trying to turn the valve train.
I have a few stuck lifters.