slammie: I've encountered the same issue, and until I overcame it, I found the pot to be of limited utility. Then I worked out that gravity could be augmented by air pressure. Pour in a bit through one nostril, then pinch that nostril, and blow (easy at first, until you get the feel for it). Switch sides and repeat.
If you're completely blocked, this can be problematic (back pressure forcing materials into the ear canals), so ideally you want to be seeing at least a trickle of water coming out the other side. Sometimes just being patient and letting gravity do its work will get you there. I also find that NSAIDs help, because inflammation contributes to that blockage. In fact, I should have mentioned NSAIDs earlier... whenever we're symptomatic in this family, we add ibuprophen to the mix.