Basically I'm looking for a tube tent. Tie a rope between two trees hoisting up the tent, with some stakes spreading out the bottom. It needs to keep out the bugs for summer, but I don't care about it breathing at all.
I was thinking about this when thinking about how to reduce the weight of my tent. Currently the Northface Tadpole 23.
I'm not sure you'll be able to find all you want with this approach.
In the woods of New England, we have a lot of trees but precious little flat ground to sleep on. For where I camp, I find that relying on trees to tie out a tarp becomes problematic because when I find good trees to use, the ground between them is awful. So, I start with finding a good place to put my bivy on the ground first, and then put my tarp over that spot. Most of the time, this involves using my hiking poles (or dead fall) to keep it up. If you're used to having no poles underneath, this may take some getting used to, but it is possible to adjust and I find the extra flexibility to be well worth it.
With respect to bugs.... I've been using a tarp tent and tarps for years. In my experience, if you want protection from bugs, you have 3 options which you may need to use together. 1) Get a headnet. I keep one in my "10 essentials" kit and it's always in my pack. 2) Use a bivy sack with a built in bug net. It's stuffy and not ideal but it's a way to eat your dinner without going insane. 3) Use a lightweight integrated traditional tent.
You will notice that I didn't list either using a tarp tent or a tarp tent in conjunction with a bug liner. No tarp or tarp tent is going to keep out bugs. It just won't. And by time you add a bug liner to a tarp tent, IMO you're better off in terms of weight and usability just get an ultralight fully integrated tent. For the best weight savings, look for non-free standing tents. The problem with the Tadpole (we have the grand-daddy Big Frog) is that it's freestanding and generally speaking, all free standing designs are heavier. You can easily find a 1 man integrated non-freestanding tent in the sub 3 lb range and it's very hard to cobble together a tarp tent/bug liner/ground sheet solution for less weight. The Eureka Spitfire 1 is one of several 1 man tents that get under the 3 lb mark.
For where I camp (in New England), I no longer use either a tarp tent or a tarp unless I use a bivy sack. Run off along the ground is a problem (I choose to not trench my campsites as it scars the land where I camp) and both tarps (better) and enclosable tarp tents (worse) are prone to having so much condensation under them so as to cause rain inside the tarp. I still prefer a tarp/bivy to an integrated tent at this point because I enjoy the elbow room and being close to the outside world, but IME there is a realistic weight limit that I have a hard time getting past. For me, that is right around 2.5 lbs for shelter. Most light bivies come in around 1 lb, a tarp is about 1 lb (unless you spend big $s), and then toss in cordage and stakes and I'm right around 2.5 lbs.
For what it's worth... our Big Frog tarp could be pitched without the inner tent. This relied on two things. First, there are Velcro wraps on the underside of the tarp at every pole intersection. Second, it came with (and I promptly lost) a length of webbing with grommets in it. This strap ran along the ground to hold the ends of the front arch pole from spreading out - essentially replacing the structure provided by the tent floor. You might be able to jury rig something similar with a length of parachord. The velcro wraps at the pole intersections add some rigidity too. Anyway, this might give you a way to experiment with an enclosed tarp tent.
Lastly, many tarp tent designs have loops or grommets at the top corners to allow for the possibility of hanging from a guy line or branch. The Black Diamond Beta Light (loops) and the Kelty Range Tarp (grommets) both have this feature.
But again, I prefer to use poles for greater flexibility in location choice.