It should go in with a tail low configuration then lift the tail up over the cross member. If the floor cover is out, putting the shifter back in is relatively simple with tower on or top removed. If the tower top is removed the make a cardboard cover to keep crap out. Having the radiator out should be adequate. It's been many years since I did an install in an F1. If you put engine in first, it will require support at the rear of it to get the trans back in. It really needs an extra hand but a single person may be able to do it.
I've pulled engine and transmission out of my 1951 Mercury cars with the radiator, the top of the core support, and the rear mount member removed with no problems and their transmission is longer than an F1 plus they have a larger cross member & K-members. If pulling transmission only, Ford had a special frame to hold the engine and then trans comes out the top with the floor cover removed. A floor jack on the pan is risky but it can be done.