My mill has a similar design as those. There is flex in the system (not backlash). The ball nut has no radial rigidity which the design needs. If you make your own add in a small linear rail/guide to keep yoke perpendicular to quill.
Most Bridgeport Z axis ballscrew conversions such as the Elrod (shown in the Centroid link), Southwestern Industries etc have the ballscew hanging way out the front of the machine, to clear the original feed stop mechanism. This isn't ideal. However, you can actually fit a 16mm ballscrew where the threaded feed stop bar was originally fitted. This reduces the overhang and gives you a more rigid result.
Here's how I did mine Z axis MkII Works nicely.
Here's another example, with the motor driving the ballscrew from above.
The skill is to minimise how much quill travel you lose, as this is a key drawback of CNC turret mills. My final version has almost the original 5" mechanical travel, although you will lose some of that due to the limit and home switches.