My thanks to the people that clarified for me where Qt and GL (Mesa) are used in Google Earth. The earth canvas itself is coming from GL. The first thing I did was try and install an updated version of Mesa built on OS 11. That made things even worse. I then installed the version that shipped with OS 11.1 and it's rock solid. No blinking, no font problems, no areas of the screen turning white.
That Mesa update, along with using newer Qt libraries has produced a very nice looking UI with anti-aliased fonts. Now all I need to do is QA the ability to launch Firefox and Evolution from within the software, and it's ready for deployment.
Update: Interestingly, using the trick to soft link in the new Qt libraries for anti-aliased fonts breaks printing and the edit >> copy image feature. I suspect that users will kind of need that. :) I have reverted back to the shipped Qt libraries and things are running well. I have not been able to figure out exactly what GE does when you click on the email button. It's supposed to pass the mailto: tag to Firefox, which it seems not to do. $BROWSER pointing to Firefox doesn't seem to help either. The File >> View In Google Maps option works fine and calls Firefox. Time to strace and see what it's doing.
[ Shot of GE with stock Qt libraries, sorry to see anti-aliasing gone]