A secondary nut at the back of the cross slide would work, but you'd need to make something to mount the nut.
I've done something like this two different ways -- one for my mill and one for the cross slide on my lathe.? My mill separate-nut approach uses a steel plate bolted on to the right side of the saddle.? The plate has a hole for the feed screw to pass through, and the separate nut is threaded down the feed screw until it fetches up against the plate.? Adjusting it removes the backlash, and to fix it in place I use a piano-wire finger that fits into a hole drilled in the nut.? Here's a photo of it:
My anti-backlash scheme for the mill is very similar to the approach Sherline uses on their mills.? I saw it and adapted it to my mill so can't claim originality, other than adding something like it to my Sieg SX2 mini mill.? My upgrade has been working fine for several years.? With it I can perform climb milling so it really does take care of backlash.
For my lathe cross slide I took a different approach (sorry, no photos for this one).? I cut the bronze nut in half along its width (right between the two threaded holes in the nut), then made a shim to get the nut heights to match the feed screw height. This way the nuts can be hard-mounted to the cross slide using the preexisting holes in the cross slide (this is a LOT better than the funky 3-screw OEM method).? I threaded the two nuts onto the feed screw, with a light spring in between them to remove the slack as needed -- to do that, one of the mounting screws is loosened so the spring forces the nut away from its neighbor, then the screw is re-tightened so the system can handle cutting forces without significant deflection.? This can be done from the top of the cross slide so it really is easy-peasy.
I like the spring-adjustment method because all the threads will bear evenly on the screw.? A nut that is split lengthwise and tightened down will only engage the screw on either side of the split so wear is concentrated there.? My scheme is based on the spring-loaded anti-backlash ACME screws I've seen...but it should be much "stiffer" because the nuts are fixed in place when in use.
Right now there's enough clearance in the nut mounting holes to accommodate the needed displacement but it wouldn't be difficult to machine a slot for more adjustment range.
