If your body weight allows you to go to the lighter model hammock, then you can include a tarp tent, or micro tent and stay within reasonable overall weight limits. This makes sense if the reason for carrying a ham. is more related to finding ideal campgrounds stealth or otherwise. I have found myself in places where only a bivy would work and a ham. would have been great, I also have been in places where a tent is ideal.
It might work out to use a tarp only when you can't ham., if the reason you need to sleep on the ground is that there isn't any vegitation, maybe the bugs wouldn't be so bad. Hams. have a tarp or the weight of a proper one for ground use is not too great.
Right now I am carrying a hammock and a micro tent. Overall weight is about what a light 2 person tent weighs. Only downside is that neither is wonderful in extended bad weather.
There is a lot of nonsense about sleeping in hammocks being more comfortable that sleeping on the ground. There are rough patches of ground, but in decades of camping I have only rarely actually slept on an uncomfortable surface. It takes very little room to build a comfortable bed. As long as the torso area is clear the rest can be worked out. I usually sleep better in a tent on the ground than at home, unless it is really hot. Stokel, who is comited to his ham., recently reported from Europe that he was surprised how comfortable he was sleeping on the ground one night. I didn't get the feeling he was more comfortable, but as long as one can sleep and don't wake up too stiff, the fresh air and often longer nights are very acceptable whether in a tree or on the ground.
Based on what you describe, if I was limited to one shelter it would be a tent.