A couple of things to note that might help you self diagnose...
Firstly, that first GOTO (before any plate solving) is a purely mechanical movement; commands to go to an RA and Dec from the ASIAIR to the mount is done before syncing the position of the mount as computed by ASIAIR.
The fact that you have an approximate location tells us that homing is pretty much working, your Polar Alignment is decent, and more importantly, the RA of your mount is equal to the Local Sidereal Time (LST) when the OTA is pointed to the Meridian. The last item tells us the Local Sidereal Time is OK. RA is made up of two values, the hour angle (HA) of the mount (HA is zero when the OTA is pointed at Meridian, no matter what time it is) and the LST is also OK. LST is usually computed from UTC (time at Greenwich), the UTC offset and the local Longitude. So Longitude must be correct too.
You can try to confirm by doing a second GOTO to a different object after a plate solve of the first object, but turn off the auto GOT centering and do not sync the mount.
My guess is that once you sync the mount to the ASIAIR coordinates is where things went haywire.
So, try to do this after a plate solve but without SYNCing (just hit the Cancel button). Take a look at the RA and Declination and Local Sidereal Time in your Hand Controller (LST is probably the culprit, but we might as well note down everything.
Now go to Telescope Setup and check the RA and Dec as reported by ASIAIR (it is probably correct), but unfortunately, ASIAIR does not report what it thinks is the LST. (That would have help diagnose the problem for everyone, even beginners.)
Next, do a plate solve and this time apply the SYNC the mount.
What happened to the RA, DEC, Longitude and LST in the hand controller? Did the LST change by about an hour? (If so, you probably forgot to turn the Daylight Saving Time off on your mount (in ASIAIR instructions) and did not set the mount's UTC offset to your UTC offset in Winter (Standard Time). ASIAIR does not understand Daylight Saving Time, and you need to use Standard Time (Winter time) n your mount.
If the LST after a SYNC is an hour off, then all heck breaks lose after that since the mount thinks it is an hour away from where it should be.
If your hand controller does not show LST (last time I used anything from Meade was at least 10 years ago, so I no longer recall if LST is available), check the UTC and UTC Offset in your mount in lieu of LST.
Try this to see if it is something obvious.
My initial guess is the Daylight Saving time thing, but it could also be bad longitude that is pushed by ASIAIR to your mount. Or, bogus RA and DEC pushed from the ASIAIR to the mount.
The short answer is to check Daylight Saving Time (DST) first. It may be the answer to your problem.
The documentation from ZWO is very scant (close to non-existent). Because of that, you need to read every fine print that they do document. One of the fine print items is to turn Daylight Saving Time off on the mount. I do not understand why they can't get Daylight Saving Time implemented since it is in iOS and iPadOS (I don't know about Android; I don't use it) and should just involve a few lines of code using the Cocoa NSTimeZone API. I am "lucky" that my mount (RainbowAstro) also does not understand DST, so the two are in sync :-).
Chen