Chances are your screws are TR14x3 14mm dia 3mm pitch so like John says you could go with RM1605 and increase speeds slightly and loose some resolution. . . . OR go the other way and use RM1204 12mm Dia 4mm pitch which if your doing mainly PCB work could suit better.?
The thinner screws won't matter here because the length isn't great and the screw speeds won't be high causing whipping. The finer pitch will give slightly more speed than TR14/3 but not much.

I think your main weak area here will be the end fixing.? Chances are they just used standard deep grove bearings which will allow a certain amount of end float there reducing accuracy ballscrews give. So suggest you don't go rushing into ordering without checking out how your going to adapt or get round such an issue.
Could be has simple as change of bearings to pair of angular contact if they fit in same space but could also mean completely different approach and need some bearing blocks making or buying.?