[Question] Replace mechanical movement with quartz?

I've got a vintage Timex Sprite that I got off eBay. I really like it; it looks great and feels great, it's definitely a watch I'll keep in my collection.

Its Achilles' Heel is the Timex movement; it's old and inaccurate, which I knew and accepted when I first got the watch, but now the movement isn't running at all. I tried bringing it to a watch shop to fix it but they won't touch it, they have no experience with old Timex movements.

I don't want to simply label the watch junk and throw it away or get another watch to replace it, I'd rather keep this one. But if the mechanical movement is not repairable, is it possible to have the movement replaced with a quartz movement instead? To me that would be ideal, a vintage watch with modern quartz reliability. It's a small watch at 30mm, so I think there should be some quartz movements that can fit it.