Is there another way to say a false dichotomy, such as a forced choice or ...?

From Wiki "A false dilemma (also called false dichotomy, false binary, black-and-white thinking, bifurcation, denying a conjunct, the either–or fallacy, fallacy of exhaustive hypotheses, the fallacy of false choice, or the fallacy of the false alternative) is a type of informal fallacy that involves a situation in which only limited alternatives are considered, when in fact there is at least one additional option. The opposite of this fallacy is argument to moderation."

Any of these suggested alternatives should be acceptable, although I'm not sure any of them is more succinct or colloquially relevant than your original phrase.