The answer to this question is almost always yes in all seriousness though we put a TON of work into the documentation and it answers about 90% of the questions in this forum. Things that aren’t in there get added fairly regularly to fill gaps. If you haven’t yet I would certainly recommend perusing through it as well as the “SGP The First Week” tutorial that can be found on our support page.
This particular issue cannot be found in the documentation though…
I will say that I have a similar issue to yours if I only use Center from a Parked position. Apparently my G11 “loses it’s mind” when it’s synced very close to the pole…it’s not hard to understand why though as if your polar alignment isn’t perfect the mount will likely not be pointed right where it should be…which could be under the pole or to the side of it. Pointing at the pole is very critical and a tiny move can make your mount think that it’s “upside down”.
I don’t really get how this is happening when you’re not pointed very near the pole though…so that’s a little odd. But it sounds like you have things working well. There’s certainly no harm in slewing to the target prior to doing the Center. This will likely make your centering require less iterations to be correct.