If you want to blame the mount for its imperfections - then you don't need any centering algorithm. Just do a slew and if it lands in the wrong place - blame the mount because the problem is the mount. High end mounts with an elaborate pointing model should point within a few arc-seconds - if you spend enough.
What is missed here is that for mid-range mounts you want the slew to be FAST and PRETTY ACCURATE - but there is little need for sub 1' accuracy. So for some mounts the encoders are not tracked during the slew - and some dead reckoning is involved so that the mount lands on the target at exactly the right time. This is not trivial to do - especially when done quickly and with unknown payloads.
The SGP centering routine is fine in theory - but it makes the key assumptions that 1) syncing works in a particular way to readjust the coordinate system locally with one call - and many mounts do not work that way with sync. 2) It assumes that when a mount is told to go to a particular ra/dec - it will land there exactly according to the mount's current encoder values and sync state. My mount is fine with (1) but many mounts are not. My mount is not fine with (2) - and it limits the accuracy of the sgp approach.
The approach I describe does not require elaborate state to be tracked. It only applies per target and once the target is centered the state can be forgotten.
Frank