Electing the President by national popular vote is by far the most commonly cited alternative.

> It does seem like most conversation focuses on direct democracy

It does not.

> since it’s fixated on respecting the popular vote.

Electing officials by popular vote is representative democracy, not direct democracy. Direct democracy is the citizens making policy decisions by popular vote, without elected officials as intermediaries (e.g., many U.S. states use some form of ballot initiative and/or referendum system, which are – limited forms, since they still have elected legislators do most lawmaking – direct democracy.)