> So what is this problem called?

I refer to them as the problems of "transparent persistence" and
"normalization".

> What theory describes the possible
> solutions?

I'm not sure what theories, but database implementations address these
issues in practice.  Your were describing Magma exactly up until the
"loosen our definition" paragraph, however, there's no reason the
other program could not be coded to access the Magma DB or files
directly -- the complete meta-definitions are included as part of the
connection process.

> Are there classes of solutions that have similar trade-offs?
> Where can I learn more?

But, obviously you know about ODBMS's, so probably this isn't the
answer you're looking for.