RPMs fluctuating wildly when stopped

I have a 2006 Chevy Cobalt with ~155000 miles. In
the past two months, every time I stop on an
incline after driving for 15-20 miles, my RPMs drop
to 400 and it shakes uncontrollably. It has stalled
twice when doing this. I have cleaned the throttle
body, and just had my front O2, thermostat, and
radiator overflow cap changed. After the most
recent fix (O2 and all) it was fine for two days...
Until I just had to slam on the breaks on a hill,
where the RPMs went wonky again. I'm at a total
loss. What else should I check out? (No check
engine light is on.)