Question: is it possible to remove / install that Front Crossmember while the Engine is in place?
Certainly possible to remove if you have a way to support the engine. Either an overhead hoist, or possibly using a jack from underneath. One might even jack it up so the front wheels "just touch" since you'll be taking the axle out from underneath anyway.
I myself would favor an "overhead support" arrangement which does not have the possibility of denting the oil pan. A large strap around the engine might do this with less risk than my usual "Third spark plug hole" lifting eye (risk of tearing out the spark plug with the weight of half the car in addition to the weight of the engine.
Removal would be the easy part. Doubtless you will make some decisions regarding whether to weld that cross-member in, or go the traditional rivet route.
The problem with welding is one of welding "uphand" (i.e. rod above your holder/hand) for the welding on the underside - although the rest of the welding is pretty routine for someone skilled. And some welders PREFER uphand.
The problem with riveting is one of "bucking up" behind the rivets. Your backing bars might have less than optimal support unless you REALLY put some thought into it. Riveting a loose frame is challenge enough riveting only "downwards" with a couple of specialized backing bars supported by the concrete floor for the up force. Doing this "at angle" is nigh unto impossible.
Truthfully, if this car were mine, I would remove EVERYTHING and do the welding/riveting on the frame where I can rotate the frame and present the best possible situation. A lot is riding on optimal attachment.
Heh. This car IS mine - kind of. I have a loose frame upstairs which needs a REAR crossmember - which I have.
Joe K