I believe this exact topic came under discussion in EWG last week as part of the discussion on potential extensions to P2034 Partially Mutable Lambda Captures (https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p2034r4.pdf). Stronger consensus was found to see a version of the paper with extensions such as const-ref-capture.

Perhaps it would be a good idea to reach out to the authors of P2034 to see if they would collaborate on designing such extensions.

FWIW to answer your question about other qualifiers - I can see the symmetry argument for volatile, but I'd want to see a really compelling use-case to approve adding more volatile to the language.