My impression from looking at the log is that you are simply calculating the sync value yourself and keeping track of it. If so - that won't help my mount and others improve on the centering - because the problem isn't in the sync but in the slew. If you simply replace the mount's sync with your own - that won't help centering.
The centering routine needs to keep track of the difference between where it tried to slew to, and where the plate solve said it actually landed. This is very different from simply asking the mount where it is - and finding the offset from the true plate solve. When you do that, it does not include the error in the slew itself - which for me is the whole problem, and the thing that prevents the centering routine from improving after a single iteration.
I hope that makes sense - but maybe I'm missing something in what you have implemented.
Frank