Someone might find this useful, so sharing here, since it's relevant.

I wrote a small PHP library that gives you a key-value storage interface to SQlite files: https://github.com/aaviator42/StorX

I've been dogfooding for a while by using it in my side projects, and it holds up very well (mostly thanks SQLite's robustness!).

And there's a basic API too, to use it over a network: https://github.com/aaviator42/StorX-API