I have the same set of experiences. It is incredibly frustrating to both myself and my doctors since I have a family history of high blood pressure, and it is impossible for me to get a baseline measurement. Only time I have ever had normal blood pressure is when I was in the best shape of my life a decade ago, and was considerably more relaxed due to life circumstances — but I distinctively remember not being afraid during the measurement, rather than feeling any different with regards to my overall health.

Also I've fainted, or almost fainted, in an array of circumstances related to needles. My experiences range from moderately humorous to dangerous (I fainted after my first COVID shot at the wheel of my car...thankfully I knew it was coming and put it in park just in time).

Don't feel too bad about being "that guy" — while the experience is incredibly personally uncomfortable, it's actually fairly common. I've just resorted to always having someone with me who knows what may happen and informing all the people involved about my history. Not fun, but it keeps me safe.

This description actually kind of makes sense.

What could help (or could have no effect) is taking the blood pressure with the electronic device. There nobody could be next to you (entrap you) and you would have a complete control over the strap - you could take it off any time you felt uncomfortable if you just wanted to.

I have an electronic meter at home and I use it time to time to check my pressure. I can be much more relaxed and I indeed usually lay down first.

Hmm, fair enough. It is possible to measure BP at the ankle (while lying down, legs flat), although it is usually higher. If you do want to test it yourself, that's an option. Your doctor probably won't really want to bother but it's certainly worth asking if you think that would be more comfortable.