Hi, this might be a Lab thread... anyway, changing the 12AT7 will have no effect on the power tubes. Different tubes will change the sound of the amp slightly, so you may wish to try swapping out the remaining Mullard for another Brimar.
Why changing the 12AT7 would stop your amp from shutting off is a mystery though. I would suggest first checking if your amp has a bias adjustment. Second, check your wall voltage, it may be on the high side.
BTW the test he ran sounds like a transconductance test. This will not show up a bad power tube. Typical tube testers don't stress power tubes the way they are stressed in a power amp.