Also, regarding your original post, bent balance pivots are just not common on incabloc balance settings, but still possible. If it was a non-antishock watch then it would be reasonable to suggest, along with checking for a “mushroomed” or broken pivot. Occasionally you’ll come across an antishock balance setting which is fussy about seating correctly which may bind the pivot. Release the spring on the balance cock without removing the jewels and see how the amplitude responds. If it increases then it’s obvious that there’s possibly an issue with either or both settings.
If the seconds hand stops at the same point each time, then my guess would be that the sweep seconds wheel could be suspect. It could also stop in a pattern if there is an issue with how it meshes with the adjacent wheels.
Id suggest you take out the sweep seconds wheel and inspect the teeth. Also see if it is straight where the seconds hand attaches. They occasionally get slightly bent by ham-fisted watchmakers when hand fitting.
For the keyless works lubricants, don’t get too hung up over whether a grease or a heavy oil is used. Both will work fine. I have a preference for grease myself here as it’s easier to apply in some respects. The correct oiling of the main wheel train bearings is more important.
Just to prove yours isn't a fluke, here is my "almost COSC" 1970s Sekonda TV face, which I have literally just taken off my wrist, having worn it all day everyday for the last month, wound and slapped on the time grapher.
.. also giving a not too shabby performance.