That particular quote does not really support the presumption here. In that debate, as with most ratifying debates around the constitution and the bill of rights, the concern is that the federal government not usurp the ability of states to arm their militias.
That quote in context [1] clearly is about who the members of the militia are drawn from, not the implicit militia-ness of all citizens. He even states this explicitly later in the same argument: "Under the present government, all ranks of people are subject to militia duty".
In the end, they wrote what they wrote and they ratified what they ratified -- "the right of the people" and not the right of the "several states" or the "militia of the several states" as is used elsewhere in the document. So it's a right of the people, period, and "keep and bear" has a plain meaning (Scalia wrote something to the effect of "you cannot interpret 'he filled and kicked the bucket' to mean 'he filled the bucket and died').
Some state constitutions (contemporaneous and known to the authors of the constitution) carved out an explicit self-defense or individual right to arms, but this language was not encoded into the second amendment.
Whenever I encounter quotes from the constitutional ratification debates that purport to claim an individual right to keep and bear arms, on closer inspection in context, they are arguing about states vs. federal authority, not an individual right. If you choose to respond by offering other supporting quotes, please give a link to the full context and due consideration of it, because I have yet to see an actual quote that holds up.
[1] https://constitution.org/1-Constitution/rc/rat_va_13.htm