I didn't need to solder. The connector on board is fine, but it's just friction (and a piece of foam glued to the back) that keeps the cable seated in the connector. So my tearing was just the cable partially unseating.
I never had the classic, but my issue was intermittent and for a while I was convinced rebooting the watch made a difference; kinda seemed to. There's forum threads that claim memory leak causes the tearing.