The best way I can see this working now is to keep the wallet and the service separate, but have everything operate on a common standard like WebLN. That way I could use a plug-in like Alby connected to my self-custodied wallet and carry that around to any LN service to maintain a balance.
What I'd love to see is a way to segregate a wallet like Alby so that balances are maintained separately for each LN service -- so one for Stacker News, another for Zebedee, etc. This is similar to the allowance/budget feature Alby has today but extending that to give the LN service visibility and limited control of the funds in the balance. That way my balance displayed on SN, for example, would be the actual balance in my personal wallet for the site.
None of the above addresses the foundational challenge of setting up a non-custodial wallet in the first place, however, but I think it still could fill a gap.