Just my 2¢ worth.....
If you cut the cross member and make it a DIY bolt-in part there will always be extra unwanted flex in the frame, not a good thing.
Confirm which engines you have by checking their block casting numbers, at this link.
http://ford-y-block.com/Block%20identification.htm
A '55 F100 y-block could be a 239, not really worth rebuilding, if you can even find parts.
A '56 Fairlane y-block should(?) be at least a 272, and of the two current choices you seem to have, the better one to rebuild.
IMHO it's easier to remove the engine & trans together and separate them when out of the car, rather than doing it from underneath. Reinstalling the trans from underneath can be even more of a problem.
The engine oil dipstick & its tube will need to be changed to match the oil pan.
.