Another voice here for doing an April Yampa trip. Unique scenery and lots of good hiking that isn't in the guidebook. Go explore. Lowest flow for me was probably about 1500-2000; I recall we had enough current to keep moving slowly. Don't worry about sandbars, except in Island Park. You'll see them, and they're easy to go around.
Weather is the bigger deal than the water flow. You could have anything. I did two Yampa trips one year in early May. One was nice weather, the other we had snow.