Hi spaceart, you can roll back to any version without losing your settings yes, just be sure careful to not click "remove settings" during uninstall and everything will pick up where it left off. (Also, be sure to reboot after uninstall, before reinstalling.)
If you install a v5 copy on top of v6, tabs will become ungrouped.
Curious to see what's going on but indeed, we're trying it on our test machines and are not seeing this. If you'd like to submit your settings via About → Troubleshooting → Create error report, we can load your settings up and see if it's something we can reproduce.
Are you able to switch pages without issue, but just cannot move groups? Likewise, can you move individual icons, if not groups? What is your monitor arrangement situation like? (Uploading your settings will give us that exact info.)
Tyty