Doing some quick measuring, it doesn't seem like an engine hoist, leveler & the motor are going to come out with the hood in place.

With the struts disconnected, can the hood be opened farther back against the windshield, or does it have to come off the hinges completely?

when i done my engine swap yes I just removed the hood struts the hood will go on back to almost straight up I took a ratchet strap and tied mine back till done

Tis safer to remove the hood.

I agree, remove the hood.