This is gonna be complicated.
I have a lineman's belt.
I have an adjustable, removable bridge (from one side)
I carry a long tether/rappel rope. As I climb, (one sticking) I take my first step from the ground onto an aider, so I also do so with a relatively loose LB. Once I hit my steps on my stick, my LB gets cinched. Mid way up my stick I lean on my LB and set my tether and bridge, advancing the tether up the tree as I top my stick and then reset the tether. Down to the stick, remove LB. Step off the stick and hang in the saddle. Move the stick up, pinning it between my tether and the tree, as high as I can while still being able to get into the aider. Then the process repeats itself.
When I HAVE to cross a limb that I simply cannot cut, I'll do one of two things.
A) I'll rely on moving my tether above the limb (which sucks, until I starter using a screw link so I didn't have to feed the rope back through the eye) while using my LB.
B) If I'm not currently relying on my tether I will sometimes disengage it completely and use my bridge as an alternate lineman's belt. This way I'm literally never disconnected from the tree. Once I get the climb above the limb done, I switch back to my regular LB and bridge configuration.
Is this perfect? No. But I do feel pretty safe doing it. It might seem complicated but it is actually really simple and intuitive.