Well, I guess I would make an aluminum split collar about 4 inches long, bored to fit the screw OD, and bolt it onto the ballscrew wherever is convenient, maybe about three 3/8 bolts down each side. Put a pipe wrench on the collar and brace is against something solid. Probably want to do this near the ball nut so you are only putting torsional torque on the ball screw. Don't want to wrack the ball screw to the side.
For the nut, either make a pin spanner to fit, or make new or modify the nut to your spec.
From the drawings it looks like if you removed the motor mount and the two large bolts holding the ''bearing can'' in place, the whole assembly would slide out the back and you could do the whole set up on the bench. That is most likely what I would do. Easier than working with limited space.