I'm a mess with family. For work however I inhale through the mouth to fill my lungs, then another sharp intake through the nose, followed by a slow exhale through the mouth like cooling cocoa. The exhale should be long. Repeat 1-3 times until I am calm enough to excuse myself. I practiced this in non-crisis situations so it's second nature and so I can do it subtly, but it does work "out loud" with a finger held up to hold off questions). Once is usually enough. But being able to say "I'm sorry, I have to step away" or "be right back" in a calm voice, rather than that shaky-voice is clutch.
Then I do something from TIPP (reference below). I recommend having a few ready at hand for various situations. At work, I'll go run up the stairs ( Intense exercise, ideally this would be longer, but even just a minute or two helps). That or paced breathing, sounds like you already have some of those exercises queued up. Holding an ice cube is a popular one.
(not endorsing anything on this site, just for the TIPP explanation, because I'm bad with acronyms. https://footprintscommunity.org.au/resources/introduction-to-dialectal-behavioural-therapy-the-tipp-skill/
The Expanse!