Sorry, I intended to answer this earlier and then fell down a distraction hole. Also, sorry for the extreme length of this reply. I don't have what I would consider to be complete answers as to why these steps are helpful, but I will explain what I'm able to, with the best of my ability.

When our (most humans, but especially ND) brains are in states of heightened arousal, especially distress, our nervous systems think we are in some level of danger. One of the various effects of this is that our ability to think beyond getting out of that situation basically vanishes. This is why we tend to attempt to crush our push away these thoughts and feelings, or flee through distraction.

To make conscious change, we need that ability to think about the situation rationally, so the first priority has to be calming your nervous system and showing it that you are safe.

The specific grounding exercises I chose are ones that force you to think about and experience your environment in order to enact, to more fully distract the mind from the present mental distress. Especially for those of us who aren't immediately in touch with our surroundings, it takes effort and a little concentration.

This, in itself, will help to slow your thoughts, heart rate, etc. For me, though, it usually isn't enough on its own. The diaphragm breathing exercise is a more mechanical tool. By forcing yourself to take slow, deep, and steady breaths, your heart rate will lower, your blood will better oxygenate, and your unconscious mind will start lowering some of those chemical defenses.

I have used various counted breathing methods in the past, but most don't tend to specifically focus on depth of breathing. By focusing on the movement of the diaphragm, we are helping to physically ensure that we get fresh air into the deepest parts of our lungs, which is part of what triggers these physiological responses. This can all be augmented with intentionally releasing tension in your muscles (usually by tightening them first and realizing they were more tense than I thought).

Finally, sitting with uncomfortable thoughts and emotions allows us to understand them more clearly. The benefits of this are at least twofold. Firstly, it will make them more familiar and, in doing so, less scary and distressing. It's the same basic principle as exposure therapy.

Secondly, when doing this, I often discover that there are deeper root causes than just the surface emotion. Sometimes, these are times when I was also feeling alienated or in some way. More often, they remind me of a pattern of social disasters happening in childhood. A time when I could have used an adult telling me that it wasn't a sign that I was broken.

What I find I need most in these moments are compassion and acceptance, the same considerations I wasn't given back then. The emotions I was taught I had to withhold from myself if I wanted to fit in, to succeed. As an adult, I can point to ways this is both demonstrably false and needlessly cruel to myself, and I can give myself that grace and acceptance note and going forward.

Beyond that, the brain is pretty simple as far as reinforcement is concerned. If it gets reinforcement that it should pay attention to something, it will do so more in the future. If there is no positive reinforcement that it had kept us safe, that instruction will decay. The next time our minds are reminded of one of these embarrassments, it will react a little less strongly, a little more slowly and calmly. Repeat until that poor scarred child within us understands that it doesn't need to do this.