Having read through the posts, this certainly makes me think it is a timing/weak spark issue rather than carburation. I've seen this happen with some of my other bikes, but not to the extent you are describing. In one case it was a bad coil, another was bad spark plug leads.
There are plenty of cases of coils/CDIs/ignitors failing when hot, at least in the Suzuki GS and Honda CB world.
I'm new to the DR game, but thought I'd throw my point of view out there. I hope I can learn something from this for when I finally pick up my DR 350/450 setup similarly to yours.