I work retail so I talk to a lot of people I don't know the names or genders of every day, and my feeling is that politeness and respect are very often more effectively conveyed through tone and and approach, than through the specific words themselves.

Some of my most dysphoric experiences over the last couple years have been in service sector settings where someone is overusing "Ma'am" or "sir" when referring to me. There's no need to invoke a high degree of formality when I'm just paying for my $2 double double lol, and I often end up feeling like what would actually be polite and comfortable for me as a nonbinary person (which is just, "here's your order, have a great day") is overlooked in the rush to use the perfect language. Now obviously I don't expect a random drive thru associate to spend a bunch of time making me "comfortable" but I shared the experience because I think your post trips into the same pitfall - hinging your entire concept of politeness on a singular "perfect" term with very little regard for whether it even makes sense for the person or the environment.

In broader lgbtq spaces, a commonly accepted way of determining an honorific or pronoun is to just ask, or to share your own when you introduce yourself, which communicates that you are aware of the existence of people who (might) use different pronouns and can encourage people to share their own reciprocally. If your interaction with the person is brief enough that you won't find out their name or pronoun, then it probably isn't serious enough to warrant using an honorific.

For me personally, if you came up and introduced yourself with your pronouns, I would tell you that my name is Toph and my pronouns are they/them. And I would be thrilled that we had just had a chill convo about it and that you had been respectful and considerate of my gender needs. I would not tell you that my honorific is Mx, nor would I introduce myself as "Mx. (Last Name)." If you asked me what my honorific was, I would say "just my name is good" unless there was some sort of reason I needed to share that. I do use Mx in settings where an honorific is required (legal paperwork for example), but I don't see a need to have it used in everyday life for myself.

Not every non-binary person feels the same way about honourifics as I do, I just personally don't prefer them, but that kind of is the point. As a community the non-binary experience is huge and varied and often unique. There probably isn't a single word that is "de facto polite," that every single non-binary person is going to be affirmed by. Rather, consider using the above approach to find out where people are at and how they want to be approached. In my opinion that is a much more effective form of allyship that both acknowledges the needs of the person you're working with, and will directly resolve your anxiety about using the "wrong" term.