Is the Slaughter Solution constitutional?

Can the House vote to adopt a rule which “deems” that a particular bill has been passed, even if that particular bill has not been passed? If so, are there any limits to the adoption of House rules which eliminate voting on bills? For example, could the House at the start of a session adopt a rule which states that there will be no voting by individual members, and that the House during the next two years will “deem” to have been passed whatever the Speaker of the House deems to have been passed? Is the question justiciable?

I don’t have a fully-formed opinion on these topics, and would welcome well-informed comments. Please stick to this issue, not to the merits of the legislation. The most relevant constitutional text would seem to be the following:

Article I, sect. 1: All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.

Article I, sect. 5: Each House may determine the Rules of its Proceedings, . . .

Article I, sect. 7: Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States; If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it. If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent, together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law. But in all such Cases the Votes of both Houses shall be determined by Yeas and Nays, and the Names of the Persons voting for and against the Bill shall be entered on the Journal of each House respectively. If any Bill shall not be returned by the President within ten Days (Sundays excepted) after it shall have been presented to him, the Same shall be a Law, in like Manner as if he had signed it, unless the Congress by their Adjournment prevent its Return, in which Case it shall not be a Law.

Every Order, Resolution, or Vote to which the Concurrence of the Senate and House of Representatives may be necessary (except on a question of Adjournment) shall be presented to the President of the United States; and before the Same shall take Effect, shall be approved by him, or being disapproved by him, shall be repassed by two thirds of the Senate and House of Representatives, according to the Rules and Limitations prescribed in the Case of a Bill

Also seemingly relevant would be INS v. Chada (1983), which rejected the position that a section 7 cases present a non-justiciable political question. The practice at issue in Chada, the one-house veto, was far more established by practice and by statute than is the Slaughter Solution of “deeming” an unenacted bill to have been enacted.