I use a massive Losmandy HD tripod, with its 1/4” thick pipe walls, as a permanent pier, so am not that familiar with the bolts provided for the AP mount base ring, or any problems with a standard AP pier.
Can’t quite see that an uneven top rim of the pier is the final cause of the mount rocking slightly – though it could be a large part of it. However, I do agree that the necessarily - slightly oversized pier top “bolt through holes” is the final arbitrator of whether the mount base might wobble. The mount shouldn’t wobble at all if it is “perfectly balanced” – but some prefer to have it east side heavy for better tracking. Also, a slightly imperfect bolting to the pier, can suffer when moderate wind gusts hit the large surface of the scope above, and torque the stacked assembly. Nothing is perfect, but we do the best we can to mitigate such occurrences.
Your “filing down the bumps” ... was an excellent first step, glad you spotted it. I had assumed, that the AP pier tops were levelled flat on a “large machine lathe”, but it seems they may have just been “sawn-off” from plain aluminum pipe stock – the “imperfect rim” resulting from minor wobble of the pipe held in a jig under a large band saw. The thinking might be that it is just a portable pier, not something requiring its own precise machining as needed to minimize problems for imaging. Users of such portable piers will likely be using scopes “for visual observations”, rather than for imaging, so no big deal. Seems reasonable - so may be good enough.
However, an additional solution to fix the pier top wobble is adding “lock washers” – either toothed type or “split ring compression washers” between the bolt undersides and the pier surface. These would “bite into” both the bolt underside as much as biting into the aluminum pier. Don’t know, but maybe the AP-provided bolts already have corrugated “lock washer type” under surfaces, for this same purpose – unless you used some other kind of flat surface bolt. Even these special bolts might smooth out over several insertions, whereas independent lock washers are easy to replace over time.
Doing this should prevent the bolts from sliding up & down in the pier oversized through-holes. The TKLS Losmandy pier bolts would provide an addition solution since they have a far greater surface contact with the pier than the small bolt heads that come with the pier or mount base ring. They also allow using even larger diameter “lock washers” to grip the pier surface material.
Finally, the TKLS locking bolts not only provide larger “finger grips” to hand tighten when starting them into the base ring – and are also far easier to find in deep grass at night, if you drop one – but also have much larger (and deeper) hex wrench holes to give you more leverage on a larger wrench, to really squeeze them (and the lock washers) hard, against the pier. In so doing, any unevenness in the pier top won’t really matter that much, since all this makes the mount and pier ... one rock solid unit.
I surmise your valiant efforts in levelling the bumps in the pier top has resolved your problem quite nicely, but you may want to consider the “lock washers” as an added guarantee. The down side is that the bolts lock down hard and require a similar wrench force to unscrew during disassembly.
Thanks for bringing up your discoveries and solution for the standard pier top.