JenJen thoughtfully supplied me with her method, which I've been following for the past week or so with none of the effects you mention.
Remove cap/silicon grommet (or whatever that thingy is that catches juice). Hold under warm water for 30 seconds, blow through mouthpiece end. Repeat for 10 seconds. Blow again until nothing comes out. Dry the carto outside completely, especially the battery connector end.
Then I refill using the method from the excellent vid sticky on the subject and vape away immediately. The worst I've gotten is the "gurgling" sound from overfilling (seems like different ejuices take different amounts to saturate the carto). I fix that with a light blow through from the mouthpiece side again (cap off) to get rid of some of the excess, clean/dry the battery end and vape away.
Because I strictly refill at home, I usually pop the newly filled carto onto my USB PT, take a couple of "primer puffs" and then go to town--flavor and vapor production are on par with a brand new carto.
I was initially worried about not getting all the water out but then realized the one of the components of ejuice is water, so the only real worry about not blowing it out completely would be diluting my flavor and not drying the battery contact end (would hate to short out my PT--egads8-o).