I think you need to fix a number of operational errors before we can spend a lot of time looking at this:
1. Update to the PHD2 2.6.14 release. I realize your computer doesn't have internet access but that means you have to take ownership for keeping the software up to date. That's not just PHD2 but NINA, the camera drivers, etc.
2. You're running the guide camera in 16-bit mode which is fine, but you have also set your saturation-ADU value to 255, a value appropriate for an 8-bit camera. It needs to be more like 16K.
3. You need to stop trying to pick guide stars manually. Use the auto-find star selection mechanism and let multi-star guiding do its job.
4. It looks like the RA drive system has problems, certainly too many to work well with 2.5 or 3-sec guide exposures. To identify the source of the problems, use 1-second exposures with multi-star guiding.
5. Do a long GA run, approximately two worm cycles, so we can see what the RA drive system is doing on its own. Do this on both sides of the pier. There's no need to do the backlash test for these GA runs.
6. In your later guide sessions, you were dithering every 2 minutes! This means you're spending an inordinate amount of time settling and it makes it nearly impossible for us to see what's going on.
7. The star sizes look way too large for your guider image scale. Have you followed the GA recommendation to improve focus? That needs to be done using some quantitative measurement process, not just by eye. The Star Profile tool can help with that.
I think you need to take the view that there are mechanical problems with the mount at this point and you will need to invest time in systematically identifying them rather than trying to do imaging. Maybe you can get that done during moony periods when you don't want to image. You can also quit worrying about polar alignment, what you have here looks fine and has nothing to do with the problems you're experiencing.
Regards,
Bruce