Interesting form of dictatorship you got there...
A discharge petition signed by 218 members (or more) from any party is the only way to force consideration of a bill that does not have the support of the Speaker. However, discharge petitions are rarely successful, as a member of the majority party defying their party's leadership by signing a discharge petition can expect retribution from the leadership.
So if they rebel against the Dictator^W Speaker, they get kicked in the nuts by their party leaders. Why do you need members of Congress again? They should just stay home and let the Speaker vote for them.
Which part of the law allowed the Speaker to impose this "majority of the majority" rule anyway? Wikipedia says it's "an informal governing principle used by Republican Speakers of the House of Representatives since the mid-1990s to maintain their speakerships". I take "informal" to mean "because that's how I like it", but not like "and you can't do anything about it". USA being the land of lawsuits, I'd assume this would have gone to court by now - or something.
Unlike some Westminster system parliaments, in which the office of Speaker is considered non-partisan, in the United States the Speaker of the House is a leadership position and the office-holder actively works to set the majority party's legislative agenda. The Speaker usually does not personally preside over debates, instead delegating the duty to members of the House from the majority party.
(That's from Speaker of the United States House of Representatives)