Finding a hitch that will work for SRT has been the holy grail of tree climbing for many years. It hasn't been found. You can use any of the hitches you describe for ascent only but will not be able to descend on them SRT, as you noticed they bite too hard on the rope. and as you mentioned if you overcome the hard grip of the hitch you have a quick trip to the ground. If you add a figure 8 or ATC to your minimalist kit you'll have the descent part worked out but in tree climbing you have a fairly complicated switchover from ascent to descent especially if you don't have contact with the tree, or for example you're being attacked by wasps.
In general you're going to have tremendous difficulty climbing tropical or temperate zone forest trees with a 20' rope. So when you say you want to be able to climb the majority of the trees you encounter with a 20' rope, that will not be the case. Climbing SRT you'll need to have a limb within say 16-18' (assuming some of the rope is taken up in a knot like a running bowline to anchor your rope) reach of the ground or anywhere in the crown of the tree.
Lastly, minimalist tree climbing techniques. I've climbed with several committed minimalist tree climbers. When it comes to tree climbing it is always good to have plan A, B and C. In other words, trees are a highly variable environment, you can have a plan and you can expect to have that plan not work. You need to have a response, plan B and C etc. The more minimal your kit is, the more difficult it is to come up with B and C.
My recommendation is to learn proven and widely accepted tree climbing technique and then pare your kit down from there. Otherwise you're building your system and technique without the knowledge and experience to understand how and what you need to respond to all the many difficulties that occur climbing.
Good luck and keep posting questions!
-AJ
