Motas, sounds like you want to rig up something like this:
the Chrysalis Bridge hammock, or at least it's cover. It has some kind of venting system built in, not sure how well it works condensation wise. But I guess it must be OK.
But I think this hammock has a coated ( waterproof) bottom. You want to know how to accomplish this with the HH. So keep in mind you will also have to protect the bottom from rain. To do that without some kind of tarp, which extends down closer to and is staked to the ground, you will have to some how waterproof the bottom of the hammock. Even with some small tarps, it can sometimes be a challenge to keep wind blown sideways rain from getting the hammock wet.
An HH SuperShelter, with it's undercover, pretty much solves that on the bottom of the hammock, but still requires a tarp for the top. A top cover- or the stock tarp - could probably be rigged/modded to come down, cover the hammock and undercover and stay put in the wind without stakes, and you could enter through the bottom.
But as others have said, condensation is going to be a real challenge. It is almost guaranteed to be a problem. Some people ( not all, and not me so far) already complain of this problem just trying to use the undercover, even when adding a vapor barrier/space blanket close to your body( should keep the SB warm and should = no condensation). But any condensation problems will likely be much worse above you than down in the undercover. Your warm exhaled vapor- plus what your body gives off 24/7 - rises. When it hits a cold enough layer(tarp, over cover), it will condense, just like it does on a wind shield. The less ventilation - which should move some of that vapor out before it can condense on the cold cover- the worse the problem.
Any way, if you figure out a way to rig it up, let us know how it works! Always looking for new solutions around here.