There are private furnished rentals in D.C.
If you have like $5K a month to spend, I'd - sign a month-long furnished lease and tour apartment buildings during that time.
30 days at the AKA D.C. furnished apartments is $4,800 including parking. Since business travel is dead - they'll probably be willing to negotiate a flat-rate if you're looking for a 30-day package too. So maybe $4,000 even?
https://www.stayaka.com/