To upgrade from mortise locks, the biggest problem is coping with that huge cavity created when the Rimlock (Mortise Lock) is removed. The biggest problem that I see is that other than filling the mortise cavity with wood, there is no connecting surface for the two Faceplate screws.
My first steps would be to first see whether or not a conversion kit
could be installed.
They are cheap enough to try just buy one to see if it will work on your doors.
To convert to the newer tubular style door locks I would see whether or not a Mortise Lock Conversion Door Filler Plate
would work for me. Note that on this plate the two holes to mount the Faceplate are threaded for the included screws. Again, I would start out buying just one to try it.