I have an odd problem that the local hardware store associates couldn't answer for me.

I have an old American Brass style shower with independent handles for hot and cold. Earlier this week they were leaking even when shut off. I have replaced the valve stems and that stopped the leaking but another problem persists.

When I turn these handles on they keep turning until they are open all the way, making it impossible to adjust the temperature. What would be causing this and is there any way to fix it without ripping out all the plumbing and switching to a pressure balanced system (our funds for home repairs are limited right now).