Ritz Tysons Corner VA frequently has rates in the 200s, even 100s on occasion. Weirdly enough it doesn’t show up when you search in VA though only DC. $100 property & $60 breakfast credit if 2 guests, I nearly broke even on my last stay.
DC actually has quite a few options sub $350 regularly: Watergate, Conrad, Park Hyatt, St. Regis.
Sometimes on slower days even the Mandarin Oriental & DC Ritz