I have more patience for hardware than I should, but I like what OC said as I don't think it's too healthy for others to obsess over this sort of stuff. To me it'd be a fun puzzle to figure out, but could be considered corporal punishment in some states to think you'd find it fun
It's good you mention that you feel
it's slowing down the more you game on it. That could lead to not just the Video card having some issues, but also the system as a whole could be showing some other related issue. As an example, it could be your page file getting hit rather than system memory causing the slow down. Several of the other issues you've listed really point to overheating, while a couple aren't heating, while another stated issue could be yet another issue...see what I mean? All info and general observations (feelings) can be important.
Since most seems to be a heating issue (IMO) and the 7600GS isn't exactly a spring chicken, I can assume the thermal paste has a large chance of being dried up and fairly useless. Example: I have a 7600GS that's passive. It usually ran hot during a good gaming stint but still performed on par. A couple years back it started bugging out on me. When I put my hand on the sink it wasn't as hot as I remember it. Not being hot could mean that it's not transferring heat well and worth looking into. Took it apart and the pink goo was dust. After reapplying some paste it's back to normal.
Have some compound handy and give it a look. Your sink may be covering and cooling some memory too, so don't overlook those. If anything, you can then rule out heat and have piece of mind that you have fresh goop in there.