a great mod with over 10M downloads called "Crawl" (https://www.curseforge.com/minecraft/mc-mods/crawl) adds a keybind that when pressed you starts crawling, however FirstPersonModel does not show your arms moving, as it does in vanilla crawling;

(the crawling animation in third person)

(the crawling animation in first person)

fom my tests, with the Crawl mod your body is a little more forward than in the vanilla crawl, I don't know if that would be a problem

using FirstPersonModel 2.3.4-1.20.1 - Fabric // Crawl 0.12.0

need compatibility

There is nothing I can do about this. This is up to the crawl mod.