I think I have a refutation here.
According to your post, Root argued: "You will have declared that two thirds of a quorum of each House of the Congress, plus a majority of a quorum of each of the two Houses of the Legislatures of three fourths of the States, may enact any legislation they please without any reference to the limitations of the Constitution, including the Bill of Rights itself."
That tracks the language of Article V of the U.S. Const.: "The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States," with the exception of the word "quorum."
I assume Root was, therefor, arguing that a quorum was insufficient to the purpose. Was it?
I found
this case where the Senate record concerning the vote proposing the Bill of Rights itself was quoted: "'Resolved: That the Senate do concur in the resolve of the House of Representatives on 'articles to be proposed to the Legislatures of the states as amendments to the Constitution of the United States,' with amendments;
two-thirds of the Senators present concurring therein.' 1st Cong. (1st Sess.) September 9, 1789, Senate Journal, 77." (Emphasis mine)
Likewise for the House: "'A message from the House of Representatives. Mr. Beckley, their clerk, brought up a resolve of the House of this date, to agree to the ... amendments proposed by the Senate to 'Articles of amendment to be proposed to the Legislatures of the several states as amendments to the Constitution of the United States,' ... ;
two- thirds of the members present concurring on each vote. ...' 1st Cong. (1st Sess.) Sept. 21, 1789, Senate Journal, 83."
If a two-thirds of a quorum was all that was necessary to ratify the first ten amendments, there seems little justification for claiming more would be needed for the eighteenth.