The trucks came assembled so I did not have them apart but there is room for the axle to slide back and forth in the sideframes
You will want to take them apart and look at the finish inside the ‘journal box’ recesses. My experience with PSC trucks is very old, but as I recall they drilled these with a fairly coarse surface finish and didn’t subsequently lap or finish the cones. I think in the kits you were lucky to find they’d dimpled the sideframe castings as a kind of pilot for you to drill and finish yourself.
I believe they are at 60 degrees which should simplify finding (or making) tools to get a better finish in these cones. I suspect there are both cutters (like the truck tuners for plastic sideframes) and laps available. You might get success with wooden laps and a sequence of finer abrasives as for track gleaming, finished off with burnishing; it might be that simply beveling the end of a paper Q-tip shaft or lollipop stick, chucking in a drill or Dremel (or working by hand), and some repeated dipping in Brasso would get you to a good enough finish in there. Be sure to get rid of all trace of abrasive when done with a given grit, which takes much longer with Brasso than you think.
Then try the tiny bit of light grease, and run the trucks in for a while, then clean and relubricate.
Light grease would work better than light oil because the cone and the pointed axle end aren’t machined to the same angle. That increases the pressure on the surfaces that do touch. The axle rides in the frame on a part of an arc. More accurately, the cone recess in the frame rides the top portion of the tapered axle end resulting in higher pressure on any lubricant than if the two surfaces were machined to match. The observed end play would only occur with the axle unloaded. In operation the axle end would tend to ride under the same point in the frame. The side forces acting on model trucks are very low.
If the cone is not smooth then even more reason to use light grease.