This sort of situation, passengers boarded, need to release seats for operational reasons, can't be unprecedented as WC implies, so presumably training recognises that there may be occasions were inducement fail. Can I ask you professionals what the Plan B is to deal with this and when can physical measures on a passenger be requested?
There is no "plan B" but there are a great many sensible options you can employ to prevent this type of cascade management failure. Many of the options are simply common sense and you could come up with them yourself. Try asking nicely. Try asking somebody else. Contact operations and reverse the causal problem. Get the captain to explain the problem which often gets a result that perhaps it didn't earlier. If all else fails then you have a " technical" problem and may need to bite the bullet and deplane everybody, where the situation is subsequently sorted out in the terminal (where perhaps it should have been in the first place). There are so many options and most of them require common sense, flexibility, and good communication.
I would make the point that similar problems are an everyday occurrence and are dealt with utilising these very same resources by professional aircrew everywhere and everyday. When stubbornness and intransigence is simply met by digging heels in and showing whose boss you get the first management failure. When (very unusually) you get a cascade failure, the danger is that something like this will result.