If I'm cut off, it is appealable to the House, right?
The Standing Orders say that if a time limit is imposed without the consent of the committee or there's a limitation on someone's ability to speak, it can be raised in the House and the Speaker will nullify subsequent proceedings. Further, the Standing Orders also say that a decision by the chair in respect to time limits or number of times a member is speaking is not subject to a challenge to the chair.
Therefore, Mr. Bittle is actually not able to challenge the chair because of what the Standing Orders say.