I know I've already chipped in my 2c, but I have been thinking about this quite a lot (lol, obsessive myself? ha, never!), so I've had a few more thoughts. I hope this isn't all too obvious or condescending, but here goes anyway:
It seems the root of the issue is one of emotional control ("the mental game" as it is sometimes referred) . You're clearly aware that these emotional responses aren't conducive to actual progress, but it sounds like you're lacking effective tactics to deal with these responses.
There's two parts of the brain that matter here, the limbic system, which creates the emotional responses, and the prefrontal cortex (PFC), which is where thought and executive function comes from. In adults, when developed, the prefrontal cortex can act to dampen the limbic system. e.g. when you're watching a scary movie, you don't actually get fully scared, because your PFC can shut down the limbic system enough, so you don't actually panic etc. Little kids on the other hand can get PROFOUNDLY affected by scary movies, giving them nightmares etc etc, because the PFC is not well developed before adulthood.
But even in adults, it's just like a muscle. It needs to be activated, trained and refined to be effective.
One hard bit is remembering when to use it, in the heat of the moment: "Aha! I'm feeling embarrassed, this must be a good time to use my PFC!" . Maybe need to work on this off-ice too. e.g. watch TV News, and every time you find yourself experiencing a negative emotional reaction, think "this would be a good time to use my PFC to get back to neutral emotions". It's a game of retaining self awareness. Essentially spotting when you're getting wound up and stepping back from that.
If you reduce emotions to their physical components (e.g. some emotions cause tightness around the eyes, or nervousness classically causes "butterflies") then you can abstract the emotion to the point of meaninglessness, at which point it will cease to have any power.
If you can become "perfect" at controlling your emotions, you will become a better skater. So focus your perfectionism on that instead of directly on the skating!
Really, its just yet another part of the sport that you've got to work on. Developed and trained like everything else.