I get all that you are saying jazz, and i agree that petesos would be better placed if he had a better machine , but it seems to me that in his current circumstances it could be not too hard a job to fit ball screw and BK nut. From what I see the BK bearing could be bolted to the outer face of the cheek, with a ball screw fitted through it and secured with the preload nut outside that. The motor end would need shortened and maybe reduced depending on the coupling size , and while there would be no easy place to fit a BF Bearing the fitup would be no worse than it is now with no support.
Yes he needs to ensure that the backlash is not occurring due to a slack fit at the coupling but that should be easily visible and remedied
What we would need to establish is whether the bore retaining the existing crosshead nut would accommodate a 12-04 ball nut, https://www.bing.com/search?q=1204+b...ANNTA1&PC=U531
and dismantling to check this should not be a hard job .