There is no reason I can see why you can't go to ground with about every hammock out there. It is just a matter of using your poles, or preferably some trees or bushes that are nearby but not stout enough for hanging body weight from, to attache your tarp to. Then put down a pad, a ground cloth or both. Then you can sleep under the tarp as though you are a regular old ground dweller.
Then if you want some additional bivy like protection, add your hammock of whatever kind, bottom entry or top entry. Just tie it to the same thing you already have your tarp tied to. I have found some of the hammocks to be somewhat water resistant/DWR, though not waterproof. As they are breathable. ( unless you are using a HH Super Shelter, which is waterproof and non-breathable) So that will add at least a bit of extra wind and wind blown spray/snow protection from whatever might blow under your tarp.
If your hammock has a net and/or over cover, that will provide some additional bivy like features. First of all, it will help keep the bugs off of you. It will also some what decrease the amount of spray or snow that can come down on your face and down bag, and add a few degrees of warmth. Evey little bit helps, as long as you don't go over board with waterproofing or restricting air flow and actually cause condensation inside the hammock.
But it seems to me that other than accounting for the net, it should be close to six of one, a half dozen of the other as far as which one works best on the ground. They should all work assuming adequate tarp coverage.