I am sure smarter people than me have tried (and failed) - but I wonder if the best approach for gun control advocates is to go in the opposite direction.
One of the cardinal rules of any statutory (or constitutional) interpretation is that courts may only provide interpretation when the language is ambiguous - and thus open to interpretation. When the language is clear - the plain meaning of the language prevails.
If you take the 2nd amendment on its face - I would focus on this: "the right of the people to keep and bear Arms, shall not be infringed."
Certainly we can argue about, and thus is open to interpretation, the term "Arms". But, having decided that, "shall not be infringed" is straightforward, unambiguous, and not subject to interpretation. I would take the position that the federal government (and state governments) can not, in any way shape or form, infringe upon a persons' right to possess such arms. So, no restrictions on felons, no restrictions on mental health, no restrictions on location, no restrictions on concealed carry, no background checks, no IDs, no age limits, etc.
The idea would be to put pressure on enough people, that the 2nd Amendment - under those rules - would not be acceptable to a majority of Americans - forcing a repeal, and new Amendment - that would provide more delineated restrictions on weapon ownership.