If you can’t afford airbnbs for a couple of weeks then you likely can’t afford Adams Morgan. If you need to sign a lease before arrival I would suggest simply going to the websites of larger apartment buildings that you find on google maps, Zillow, or Redfin. You can find lower priced apartments along Connecticut avenue from Woodley Park to Van Ness. These will be walkable, safe, and metro accessible. Best of luck.

Prices just a bit over your budget but all utilities included:

https://www.quebechouseapts.com

I mean a dedicated bus lane on 7th between Penn and Mass would save more than one minute. Also, it’s about incremental changes that prioritize public transit and pedestrians over cars.