If none of the basic fixes work, what advanced troubleshooting steps can I try for Roblox error code 403?

Try performing a clean boot of your computer to rule out software conflicts. You can do this by typing 'msconfig' into the Windows search bar, going to the 'Services' tab, checking 'Hide all Microsoft services,' clicking 'Disable all,' going to the 'Startup' tab, and clicking 'Open Task Manager' to disable all startup items. Restart your computer and see if the error is resolved. If it works, re-enable services and startup items one by one to identify the culprit.