The 1842 antifilibuster rule change only affected the House. Thus the canard offered was yours.
The Senate still today requires 3/5th vote for cloture under Senate rule 22. Until 1917 there was no procedure for cloture. Though the rule for cloture could be changed by simple majority, the rule change could itself be filibustered unless cloture was enacted by two thirds of those present.
Back then, a filibuster was rare and used to change, enter, or remove an amendment. If any of that occurred, then the bill went back to the house, where as I pointed out a filibuster could not be mustered.
Without an amendment option, the chair would not recognize a Southern Senator, the vote would be tied, and the Vice-President would cast the approving vote.
That is why Senator Wigfall correctly pointed out that the balance of power was lost, regardless of your misrepresentations.
But if you want to continue to engage in revolving door speculation, go ahead
I will rely on the commentary of the time by the people involved.