You could certainly comb the fiber first to remove the neppy bits. However, the licker in will remove a lot of the shorter bits too. I'd play around with it and see which prep you prefer.
I made my own blending board and enjoy using it to make rolags where I'm combining colors and textures but not going for a super smooth prep or highly blended.
I have Valkyrie Extra Fine Combs and Hackle and I love them. These are really nice for removing vm and getting a super lovely prep...
I bought a couple of the polytrays from KW and I didn't like them. One got a bit malformed during shipping and was never quite right. At least with their metal pans you can bend them back into the correct shape. They were okay as far as lifting and carrying them goes, but I'd always worry that...
I have some rabbits who do this as a sign that they want out of my lap, generally because they need to "go to the bathroom". Some also seem to do it as a way of returning my grooming.