both hands on snare..unison train half-shuffle-ish +back beat?
That's the sound I hear when listening to Zydeco.
If you don't get any better advice, you might try playing that pattern to a few Zydeco tunes, just to establish a "feel" to work with. Then try to play a simple 2/4 beat that fits that same feel. If that works, try cutting that down to 4/4 while maintaining the same feel. Try playing straight 8's on the ride, but in a way that really suggests a swing or shuffle (if that makes sense). If you want to get fancy, try playing a tiny bit of clave pattern on the snare for added syncopation.
Then try to change up the patterns every few bars without losing the initial feel that you've described.
If you can do that, you're probably at a good starting point.
And don't be surprised if half the set calls for a traditional R&B approach to drumming.