I guess the closest I come to drying on paper plates is to use "basket-shaped" coffee filters.
I put a square of paper or card stock into the coffee filter along with the drying seed heads or seed pods. I write the variety and date on the card stock, not the coffee filter, so i can pour it along with the seeds into envelopes for ongoing drying.
Actually, I write the name and date on card stock before I go outside to harvest. Then I just pour the label along with the seeds from coffee filter to envelope to Ziploc. Desiccants may get involved somewhere along the way.
The stand-up pleated part of a basket coffee filter keeps breezes from blowing seeds around as they dry, but they do nothing to abate the disasters that a curious cat can cause. Hence paper-clipped envelopes.
Maybe re-seal-able envelope flaps would be a plus, but I just save the "return" envelopes when I get bills. Even a torn-open envelope can be used for drying/storing seeds, but you have to fold the top over before paper-clipping it.
>> collecting seeds that aren't yet dry. In your climate, that's probably all the time!
Mid-summer would be an exception. We usually have dry-ish summers.
However, in fall I sometimes have to collect seed heads in the rain, then wrap them in coffee filters and cotton towels, then press them to wring the rain water out. Then dry them "air-dry". Then the ACTUAL drying phase starts!