Graphical Glitches and Tears during gameplay (Xbox 360 E-74 error)

This is a really weird problem, so here it goes. I recently got my Xbox 360 fixed for an E-74 error which usually means a GPU problem or HANA chip problem (as best to my knowledge) by someone the does repairs professionally. I got it back and a few weeks later the E-74 came back, so I decided to take matters into my own hands and fixed it myself. I took apart the system, cleaned up the thermal paste, and took a heat gun to my system after warming it as some guides have recommended for the "do it yourself" fixes (it was really wonky) and it seemed to work, but for only a day. This is of course after I reapplied thermal paste and put it all back together.

Here's where it gets really weird; I still get the E-74 error, but only after I play a game. I'll be playing a game and maybe ten to fifteen minutes into the game I'll get pixelated graphical problems (black and white pixel boxes appearing, followed by purple ones, then multicolored lines across the tv, etc.), but the game will never, ever freeze. I can play indefinitely, but the moment I turn my Xbox 360 off and try to turn it back on then *poof* E-74 error. When I unplug the AV cable and power and let it sit for thirty minutes to an hour, sometimes longer, then plug everything back in and start it up then, like magic, I can play the system and play a game! But the process will repeat itself; ten to fifteen minutes later I get graphical errors that vary in severity, I can play whatever game is in the drive for however long I want, but the moment I turn it off and turn it back on I get the E-74 error. Unplug, let sit, rinse and repeat.

My Xbox 360 is the falcon board, but I'm using the Core series power brick and AV cable, a 120 GB HDD that I bought from gamestop a few years back, and a wired Xbox 360 controller. My 360, as I said before, has been repaired before, I put Arctic Thermal 5 where the GPU and CPU go, and every screw is accounted for. Does anyone have any answers as to why this may be happening?