All in the name of “maintaining a well-regulated militia”.
I think therein lies the solution. The 2nd Amendment has two parts:
a) People should be free to bear arms;
b) So that they're effective members of a well-regulated militia.
Why defend only "a", but not "b"? Enforce "b"! Have a permanent, universal draft in the US, as is done in other countries. 1 to 3 years of mandatory army service when one turns 16 or 18 years old, including obligatory extensive firearms training and infantry tactics. This way everyone will be a full part of the well-regulated militia, making their free arms-bearing when released from the draft a useful skill to both family, neighbors, State, and Union, in the eventuality of external invasion.
Complement it with two provisions:
c) Once one's released from the draft, one gets, to keep and safeguard, the personal-grade weapons and body armor they used during their draft, with a legal duty to keep them in working order so former draftees can be called unto service ready for deployment when duty calls. They may also bring to service any additional weapons and armor they own as personal belongings if they so wish, but, at the bare minimum, they must have their government-issued ones always in perfect functioning order -- and always ready to be inspected.
d) One may refuse "b", and be exempted from the draft (and also from "c"), but that automatically rescinds their "a", as they cannot be split. Hence, if someone wants the right to bear arms, one must be part of a legally valid militia by following all the regulations that make it well-regulated.
Those provisions would simultaneously completely fulfill the 2nd Amendment's original intent Conservatives are fond of, and reduce accidental gun accidents and crime as Progressives desire since every single arms-bearing citizen would be fully competent at it. It'd also fulfill Communists' and Anarchists' wishes since all Proletarians would be armed and ready for the Revolution if conditions are met; militant Feminists, since all cis-women and transgender persons would be trained to be ready to defend themselves with full force if attacked; and also provide the means and training for all members minorities to similarly defend themselves.
No Constitutional changes are required, only ordinary laws, if even that much.