"Green" seeds are and can be problematical. My own experience has not been good generally. Best to let nature mature them. If you pick "too" green you are usually not successful in my experience. Here the problem is not moisture per se, but maturity or ripeness. There can be exceptions. In cases I have succeeded, it was was placing the seeds on paper towel and in indirect light. Never place in a plastic bag in direct sunlight. That WILL fail.
You say "My perspective is mostly on what to do with literally soggy seed heads". A question. Why not let nature dry them on the plant? Am I missing something?
I do concur with the general comments of the original post.
Seeds that typically must be used fresh are usually tropical. And yes, if you dry them, they will be useless.
