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For celestron mounts the firmware designer has stated it is largely an issue of timing in landing the mount at the right place at the right time. You can read the documentation on "Calibrate GoTo" - it is designed to tune the GoTo timing for the given mount and payload to compensate for this variation. This would have explained and potentially solved the problem for celestron mounts - but unfortunately the firmware has changed so that this feature is not supported - in exchange for faster and more consistent slews.
If the miss is repeatable - for any mount and for any reason - there is good reason to think it can be compensated for in a subsequent slew. I see no reason not to expect this.
And if you are truly in a regime where the mount is missing the target randomly in successive slews - with no consistent offset - then you at least have a chance to hit very close after a few tries. It wouldn't "converge" but it has a good chance to "eventually reach."
But as it is - I expect it actually to converge rapidly and with less error - for any mount that for some reason shows a consistent offset in the sgp centering routine.
Isn't there anyone who can try the new code? I cannot - unfortunately. Even without the code - as I described above you can ask a mount to goto a particular ra/dec a few times and note the offset. If it is consistent, tell it to go to a slightly different ra/dec to compensate - and see if it improves the final result. No ascom or sgp involved - just the mount doing its thing.
Frank