I would think you'd need zero flute cutters, Paul. Not sure why 3/16" wouldn't work on HDPE as long as your speed/feed matches the bit. How long are the axles? If they're very long my guess is you'll need to take light cuts to limit deflection in the center.
For that small radii in the corners you're going to need a really tiny bit and I would probably do it with two bits - one to get the shape and a smaller one for the corners.