In Step 8 we found some backlash and reduced it by tightening the end nuts, but that's not a perfect solution - too tight and the nuts bind up as the shaft spins, too loose and the thing comes undone again!
So, I bought some M6 half-nuts (left-hand thread for the Y axis, normal for the X axis) to allow me to take the play out and then lock the nut in place.
I haven't fitted them yet, I am hoping to also make some new end-plates (like this guy) with deep groove bearings to improve matters further.