I think I’d try an impact next. I think in this application you’re less likely to damage it with an impact. I’m in the fortunate position of having multiple impacts to choose from, so I’d work my way up, but I think a 3/8 impact might yield success. I haven’t done mine, are you sure you have exact the right bit? There are like three variations of torx and none are “10mm”. Is it a 10mm Allen?
I had this issue. In the end I bought a cheap toaster welder and learned how to weld (poorly) and eventually got a good enough weld on a coupler nut to twist it out.
Getting a shop to do it is $50 cheaper, but now I have a hobby welder to play with for other stuff.