I could gather from article in Breitbart that the Constitutional POINT OF ORDER vote would not need a revote in the House but that Warren could attempt to get an amendment for her cause on campaign finance requiring a vote in the house. Not so for Cruz maybe there’s another ace card...deals with libs to get the Warren amendment to the Senate floor...forcing a revote for cromnibus overall thus blocking all the measures...not sure
I think your analysis is correct. Fun times, maybe.