I am wondering about a few things.
When you received this, you said that the original owner replaced the PS and, "we" were assuming that the replacement created the problem (different polarity). So, do you know exactly why the original owner needed to get a replacement? Did they lose the original power supply? Did it go bad? Did the mixer have a few problems and the thinking was that a replacement PS would solve them? I am wondering if the mixer has problems apart from the power supply.
Is it feasible to simply not use that power supply board. IOW for testing just use a known good PS - you said 12V at
So, use a good 12V power supply connecting to PH6 and PH7 and see if the mixer is working reliably and with no intermittent issues. It might help narrow down what you are dealing with.