You didn’t look at W&M? Tufts?? Richmond?? Brandeis?
I think W&L would be a fine choice but it’s much smaller. The prof we met on campus told us that after Sewanee (of all schools), that W&L places more in DC jobs on a per capita basis than anyone. I forget the exact subject, but it was Sewanee and then W&L. But it’s rural (but they do have a DC term which includes internship).
If you are looking at the set you are, why not Vandy, WUST, or Wake Forest.
But rather than look at big name schools - look at special programs. For example, my daughter is an International Scholar at College of Charleston - so she’s in a select group focused there. You can find those types of groups at various schools.
Honestly, pre-law is advising and econ can be done anywhere - but you seem name focused - so why not look at the names? Lots of schools have DC programs - in fact most - because it’s affiliated at American. But to look for in school internships, why not look in cities - so Macalester, South Carolina, GW/American - even if they’re not your top, UMD and George Mason, etc. as they are close by.
Alternatively there’s lots of LACs - wonderful schools in PA, Ohio, Maine, NY, etc.
Bottom line - the answer to your question is vast.