How many people need to tell you that moving the RF away from the back of the radio is most likely the solution before you believe it, and stop pointing fingers at the power supply?
You're obviously frustrated with this, I understand that. But you're arguing semantics when the issue here is practical application. You first thought it was the power supply as the root of the problem, which it is ...and it isn't. That model might not tolerate even the 5 watts ERP you are putting out in close proximity, and may cut out when used at particular frequencies. I see you've had your license for almost 5 years now, there are hundreds or maybe even THOUSANDS of licensees here with DOZENS of years of experience that are all going to tell you the same thing. Your antenna setup AS YOU HAVE NOW is the weakest link in your system. Buying a new power supply, as you alluded to very early on in this arduous thread, might solve that transient problem as you have...but the poor practice of having a whip on the back of a transciever unit isn't helping you. Sure a newer biggier more-better fancier power supply (RM-35 linear type) might prevent the shutdown under certain frequencies issue you're having now, but the bigger fact remains...you are exposing that current power supply and yourself to unacceptably high local RF conditions, even at 5 watts.
you can literally get a $10 dollar mag mount antenna, a length of coax and appropriate connector for that set up, stick it on a ground plane and see if the issues persist.
I'm not going to argue with you over this any more. Your current set up is not in the best practices of the hobby, that is why you are having issues. All that stuff you keep referring back to in "post #17" means nothing if you don't do it.
Get a remote antenna, some coax, some connectors...hook the radio up correctly, get some distance between your transciever and the power supply and try it again.
Good luck.