I have an extremely similar environment with a similar issue. Single PA-820 on 10.2.13-h5 with GP on loopback, with GP clients on 6.2.7. Certain users will get the certificate issue and at first thinking the certificate was the problem, I dove into troubleshooting that specifically. Upon several attempts at any fix I could find, the only solution was uninstalling and reinstalling the GP client. My support partner also could not find any solution, and we both agreed that, to save the headache, reinstalls would serve as a workaround for now. I don't believe any of the logs showed the firewall at fault and only certain users were affected while others connect flawlessly, so my issue seems to differ from yours in that regard. I only started having this issue on 10.2.13-h5 with newer GP clients (6.2.4+) and seeing that you have a different, albeit similarly adjacent issue it may be a bug within this PAN-OS release. If you find a solution let us know, I would be interested in learning more!
Also, a word of caution - I tried 11.1 on my PA-820 and it ran like absolute garbage. The release I used entirely broke my logging on the firewall. All syslog, ftp, and snmp simply stopped working without even support being able to restore it and suggested it was an 11.1 issue... I downgraded to 10.2 shortly after. I'd advise anyone to run 10.2 for as long as you can! Granted, however, this was a preferred release from ~1 year ago so perhaps they've cleaned it up by now. I'm dreading the EOL for 10.2 and the inevitable switch to 11.1.
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