I solved that quickly and easily.
But, first, what an excellent and awesome guide!!!
Now, a year or so later...
The slop of that axis (or any one of them) can be quickly solved by fixating the axle using a screw that pushes the axle against one side of the shaft. I only had slop in one axle, and of some unknown reason there is a short screw inserted to the side of the mount, perfectly aligned at the bottom of axle. I can see it in your picture just left of the shaft, on the side. I removed that one and inserted a longer one that pushes on the axle, holding it in position thus stopping the wobble of the axis. This does not at all hinder the rotation of axle as long as properly greased.
Remember to grind the screw/bolt so it is pointed at the end (see below).
Also, I put a locking nut on the screw so it does not move out, see pic.
IMG_6067.HEICIMG_6069.HEIC