The only response that matters. This city is a nonsense place.

Try Alas Lane. They are a small company of property managers who rent out privately owned single family homes in behalf of the homeowners all throughout DC and VA. Due to their size and unique business model, they may be more willing to accommodate a virtual tour request. PM me if you are interested.

Waaay under your budget but one of my favorite hidden gems is Artechouse. Immersive tech/art installation with a bar. Maybe you can make include it in a multi-part date package