Have you tried other plugs in the ST3?
The tip profile on the plug can make a difference in how well it works in a jack.
Personally I don’t consider any 3.5mm / 18th inch jack to be a heavy duty constant
use type of connector.
May consider using a small extension cable to plug into saving the wear and tear on the actual ST33 jack.
That all said if getting into an SQ (and I’m sure it’s a little more dense) is anything like a QU it would not a project to take on for your first repair job.
I wasn’t going in to repair the the ST3 but if I remember correctly it looked like the ST3, USB, headphone jack, ALT Out and headphone level were all on one smaller board. It would require soldering to replace just the jack.