I use a swivel on my spinning DS outfit, with the leader just under the 7' rod length. Other rigs, I'm 100% sure I've had fish bite on the swivel, so maybe that's the OP's problem? I'd for sure make the leader longer from swivel to hook. I virtually always do an underhand pitch with a DS rig.
FWIW, lately I've been dropshotting with a baitcaster (Tatula CT) on a Denali Attax 7'MH with straight 12 lb Sunline "Super Natural" monofil. The main reason for doing it was when I set the hook on a 4 lb. 8 oz. LM right next to a dock in probably 20' of water...barely managed to get her away from the dock and to the boat. I'm almost shocked at how well the baitcaster works, but the Tatula CT lets line peel off so easily, it just works great. The rod also works better than one might expect. Part of the reason is that's the identical rod and line that I use for a Shakyhead, so I can switch 'em off if I have trouble with one or the other. No leader, no swivel, no braid, just easier and quicker to rig.