For example, for the same MP/RPM settings on my Lycoming IO-360, bhp will
be less at best economy vs best power.

That's what my original understanding was, and why I was confused by the
presentation of the power setting table I linked to.

You can prove it simply by leaving the prop and throttle where they are, and
moving the mixture in between best econ and best power. At best econ, you
will be slower than best power. Slower = less power being produced.

If you actually could just get the same power at a lesser fuel flow without
adjusting MP and RPM, putting aside CHT considerations for the moment,
there'd never be a reason to run at best power. It'd just be burning more
fuel for the same result.