I think it might be hard, but also might depend on a lot of factors like agency rules and seniority. I know someone who took a pay cut relative to their last role and also had a private sector offer for twice more than what DC gov was offering, tried to negotiate for a bit more than the initial offer, and they didn't budge.

I haven't been to them all, but my favorite so far is Menya Hosaki in Petworth. They unfortunately have weird hours and the wait-list fills up fast, but if you can get seats it's incredible. Daikaya is also a good option.