Hi Arutha and Paul,
I was going to post here last night and re-size the pics above but was only able to get to one post then passed out for the night!
I think you are both on track. If you’ve checked the arbor and pivot for straightness and have determined that the escape wheel is running true and that tooth spacing is even (preferably check while in the movement as Arutha suggested in his previous post by removing the pallets and then under low mainspring or finger pressure power spin the train slowly while observing the truth of the escape wheel. You can use anything you wish as a background reference point while observing the tooth tips) then the most likely cause would be too much play between pivot/pivots and hole/holes. If it’s following a definite pattern ie: changes beat at the same tooth or group of teeth every time then I would suspect out of round escape wheel, problem with tooth spacing or bent pivot or arbor. If there’s no real pattern then my guess would be pivot slop. Too much play between hole and pallet arbor pivot and or escape wheel pivot can cause irregular beat in most clocks but I’ve found escape wheel run out caused by one or more of the reasons mentioned above or bent or broken escape tooth tips a more common problem for me.
I hope it turns out just needing a bushing or two.
Curious to hear the results Arutha,