Eqmod's eqascom allows a user to store synch points into a model that can build a map of pointing accuracy across the sky. The settings allow you to synch without storing the synch point, to synch and store the synch point and also to either startup with the stored synch points or to startup with an empty model.
Eqmod's pointing model can interfere with plate solving and the iterative centering routine as the number of synch points build. It is unlikely to interfere with the accuracy of centering over a typical evening's imaging with slewing/centering a few targets. However if the synch points are stored and then reloaded at eqmod startup, over successive evenings' imaging, you can then get problems centering exactly as you have experienced as the internal eqmod model has sufficient number of synch points.
SGP's manual - accessible from the Main Sequence Software Support pages, http://mainsequencesoftware.com/Support, has a section devoted to Eqmod users and getting the correct settings for flipping, side of pier and pointing models. Chris Shillito's eqmod You Tube channel videos are very helpful too, https://www.youtube.com/user/chrisshillito. The advice and experience of many eqmod users is to not store and reload a model of synch points - SGP's centering routine works like a charm and you will be on target in a few iterations as you have previously experienced.
In SGP I suggest you use the 'synch' setting in the Telescope tab.
I used to use eqmod when I had an NEQ6 and then Avalon Linear Fast Reverse. I have a different mount now and no longer use eqmod.
There are many eqmod users on the forum and I'm sure someone will chime in and help if the above doesn't help you identify any erroneous settings in eqmod.