Hi Nathan - this is not an official response in any way, but FYI I was just working on a python script (hosted notebook) that crawled through my content and turned off the "Show in Field Maps" option. I have to clean it up some but I can share it with you if you want when I am done. From what I can tell (unofficially) poking around, the key is to add "FieldMapsDisabled" to the typeKeywords for the webmap.
Email me (tschwartzman@esri.com) if you want a copy. Note that it only does content for a single user, not the whole org.
Also from what I can see, turning off Field Maps access means no collection or viewing in Field Maps. I don't know if there is a way to get it in Field Maps for view only (when it has an editable layer anyway). I don't think you are asking for that, but FYI. Perhaps the team can weigh in on that.
Tom S.