I agree, collecting seeds in the Pacific NorthWet can be tricky.
When I have soggy flower-heads, I'll wrap a piece of paper towel around them to catch loose seeds, then press the bundle between cotton toweling. Press, wait, open, move the bundle to a dry spot , press again. Repeat.
Then fluff it up and give it air circulation while it dries the rest of the way.
Bags probably are better than bowls. I might try that.
BTW, when I'm collecting seeds from something big that might drop them, I use a big cardboard box with a garbage bag inside it (I don't like seeds to get trapped between the "flaps" on the bottom of a cardboard box). I get the box as close to the base of the plant as I can, then lean the flower spikes over the box so that most "escapees" will fall into the box. . Then I cut the spikes one by one and drop them into the box.