An interesting wrinkle here is that under the Treason Felony Act of 1848, any effort by Baldwin or anyone else to "compass, imagine, invent, devise, or intend to deprive or depose [the King], from the style, honour, or royal name of the imperial crown" would be a felony punishable by transportation or imprisonment for life.
On paper, that means Edward could have had Baldwin and anyone else on the record in favor of trying to force abdication arrested, tried, and imprisoned. In practice, though, it would have been politically disastrous for Edward and would probably have been used as grounds to declare Edward insane and appoint his brother Albert as regent.