For the US I'd like to see Erie class gunboats, Barnegat class seaplane tenders, and either a converted flush deck APD or a converted DE APD. None of them are DD's but I think they'd all fit under DD in game speak.
There was nothing of historical significance to base the SAs on though
Several years ago I found an account of it working with the other escorts in a convoy to chase off a U-Boat. That's the only specific reference I found.