Before you do any turning on the spindle side of the backplate, check for high spots around the counterbore holes. I bought an ER-40 chuck from PM last year and there was enough of a burr on the spindle side to prevent it from sitting flat on the spindle and left a gap when tightened. I forget the numbers, but it was in the 0.005” range. A little polishing with a sheet of sandpaper on my surface plate flattened it up enough. The runout you are getting now could be from the way you are holding it as well as your first skim cut on chuck side of the back plate.
Keep in mind, if you take a skim cut on the back of the plate, it might not sit flat against the spindle any more since the pins pull it on to the tapered bore and the spindle flat to give dual contact. If you take too much off the back, it can’t pull in enough to then also sit against the spindle flat and might allow it to sit angled on the taper. Before doing anything to it, you might want to blue the taper in the backplate and see what kind of contact it is making on the spindle taper. If the taper is not making good contact, then truing it up is unlikely to help.