I have removd/installed many engines with trans attached by myself, with an overhead hoist/cherry picker. Just took off hood/ I have to finaggled it several times but just gotta take your time. Nelps to have a helper!!
It would help to have the mast of the hoist closer to the center of the engine. Your setup with the bracket and chains is too long. An engine lift plate bolted to the intake is a far better idea.
This is a 383 and a 727 that I installed myself.
Another idea is to cut the core support above the radiator opening. You could cut a section out of another car a couple of inches wider per side and bolt it back together after the engine swap. The upper section of the core support does not provide as much support for the unibody as the lower section does.