Okay, I think I experienced something like you're describing on my second-to-last long run and forgot to mention it here. It was later on in the run and the mucus in my head had gotten to be just that thick consistency where it kind of streamed down the back of my throat in a sheet. It was pretty uncomfortable.

If you haven't got this sorted yet - and if this is the same thing - I think irrigation before a run should help a lot, both by clearing out some of the goop and by moisturizing and thinning what's left.