How much of a problem will weak LORs be?

OK, so I'm otherwise a decent candidate. For example, my GRE score is 165/167 and GMAT practice scores are 750+

However, I'm about 5 years out of undergrad and havent kept contact with my professors (who were not finance/economics related anyway), so this group is mostly out. Would it be odd to have a non-finance/economics professor write a rec?

I could also maybe get some adjuncts from a top university where I took some econ/finance/business continuing studies classes. However, I'm certain these would also be tepid. Haven't really connected with any recent professors.

I'm thinking of applying to Duke, BU, JHU, and Tufts for an econ masters and worried that LORs will derail me. Should I take some classes somewhere just for the LORs?

THANKS!