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The procedure has only been used before to make amendments to bills. --
I take it, from that comment, that you would not find the procedure to be constitutionally infirm if it was used to make amendments to HR 3590?
The constitution gives both houses the right to make the rules by which they operate. However, it also requires them to vote on the same piece of legislation, comma for comma, period for period, semicolon for semicolon, and to record the votes of each member in the official record. The Supreme Court has already decided this. So, however they get to the final piece of legislation is their business. But each house must vote on the final version of a bill, one bill at a time, and the bill the House votes on must EXACTLY match the bill the Senate votes on. That will not be the case in the bills at hand.
Article I Section 5 ... Each House may determine the Rules of its Proceedings....
Article I Section 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 ... 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....