I'm on the spectrum. I'm 47, and I've at least suspected that I was on the spectrum for over 30 of those years. I've been convinced of my borderline autism for a bit over 20 years. My father's side of the family has a lot of people on the spectrum or only just barely off of it. I was actually raised to not look at people in the eyes, because of the number of people in my family who are less comfortable with looking people in the eyes or being looked at in the eyes than me.

My meltdowns were similar to yours. I'm sure there were differences, but it sounds to me like there was one thing in common:

When I was having a meltdown, my panicking brain felt that the most important thing I had to do was to explain exactly what was wrong. Selective mutism was therefore seen as the worst possible outcome. It was also, "unfortunately" where I tended to go immediately on my worst meltdowns. There was no explaining it, no stimming, and all of the literalism and inability to filter was minimized because I just shut down.

But that was 24-29 years ago. And over time, I managed to have the presence of mind to reflect on how my various meltdowns went.

My worst meltdowns were really not that bad. They were generally with the person who matters most to me, but the only thing bad that really happened was I didn't speak when a response was needed. If I had known enough to apply either Peter's or Tinkeringbell's answers, they probably would have worked. As it was, I had no clue what to say about them, I didn't even really understand what happened. "Meltdown" as a symptom of autism wasn't something I even knew about until later.

But my not so bad meltdowns of 20-22 years ago were much worse. If I had not worked in an environment with a suffusion of people on spectrum, and a suffusion of people experienced with dealing with people on spectrum, I potentially could have been fired. I didn't hurt anybody, but I said very inappropriate things to people with the authority to fire me, I had barely muted screams of frustration, I stimmed in front of coworkers.

Eventually, I had the presence of mind to realize that conveying exactly what was wrong is not something I can do during a meltdown. That selective mutism? That's helpful. Embrace the selective mutism.

With some experience in embracing it, I learned that I could actually convey one sentence, which made things much better. "I can't deal with this right now." Sometimes saying that wasn't enough. The person who triggered the meltdown would insist that the situation had to be dealt with right then. My control was less good, but I managed to whimper, "I can't deal with this right now." The same sentence, but it was clearly a struggle. And that convinced them that I was serious about it, and they left.

It's been 16 years since my last really socially awkward meltdown. The few times when I had to tell someone I couldn't deal with something right then were all situations where a technical action needed to be taken. I was the expert, and I knew what the technical action needed was, at least at a high level. The person who triggered the meltdown was my boss or my boss's boss, and they wanted to know what to report.

Without them there, I was at least able to recover enough to do the technical work. I was definitely not verbal yet, but computers generally can't understand my voice anyway. I fixed the issue, then spent a long time drafting an email explaining what happened and what I did to fix it, which was very therapeutic for my sanity. Generally, after sending that email, I was back in a mental state where I could talk. If the person who triggered my meltdown was still around, I'd go to their office and poke my head in to say the problem was resolved and they had an email about it.

I like to think of myself as sophisticated about this stuff, but I actually only learned the term 'meltdown' was used to talk about this sort of thing a few years back, and only more recently realized that my meltdowns were meltdowns. But I think knowing what's going on is quite helpful.

Since I can pass for neurotypical most of the time, I have found that I can actually tell people about my borderline autism and talk about what autism is and how it affects people without getting nearly as much of the social stigma that people get when they talk about it right after they've had a meltdown or some similar issue.

I don't harp on my autism, but there's a few dozen people around who now know about my autism who aren't my coworkers. I haven't had any meltdowns at all recently, but I have seen a couple of these people react to others having meltdowns both before and after, and it's like they understand better.

TL;DR: The selective mutism is possibly the most socially acceptable aspect of the meltdowns you describe. Especially if you can combine it with a pre-prepared card, per Peter's answer, or something similar. If there's a technical situation involved, and you're the expert, you may be able to focus on that while you recover from your meltdown. Then see about apologizing, but not explaining, per Tinkeringbell's answer. After you have distance, you can explain, also per Tinkeringbell's answer. Rainbacon's answer is also good. But also remember that you can be an advocate for someone else in addition to getting some people to be advocates for you.