Hi Muzzer this is an opportune post of yours as I have a very similar problem with HTD drive to a lathe cross screw.

Small drive pulley 12 T and large 26T driving a 1605 ballscrew via a rotating ballnut.

The measured lateral backlash with the shaft locked is 40 half steps or 9.3 thou—total rubbish. I can actually see the belt moving and taking up the slack while the driven pulley is stationary.

The only reason I used HTD was the rotating ballnut came fitted with it. To be fair to the manufacturer it was designed for high speed, low force and low precision and I want the exact opposite of all 3.

To compound matters, the open loop stepper I was using on the supposed half step actually steps more like 1/3 step and then 2/3 steps. Ho Hum.

So plan is to change to AT pulleys with an ATL belt after changing the stepper motor to a closed loop one with encoder etc.

As far as I can ascertain, this combination of AT pulley and ATL belt gives the least backlash, although the availability of ATL belts is sketchy.

Cheers
David