About all I can contribute is I have been saving tomato seeds for more years than I can count. I never plant them fresh however I dry them on a paper towel and save for the next year. I always have healthy beautiful productive plants. The seeds do stick to the paper towel but you can plant the paper towel as a sheet if you like or cut up, he paper bits break down quickly.
Yeah, I also used paper towel on the latest. Those are still 2-3 weeks out from popping up. But yes, they were wet.
I had been drying some but sent them off to a friend.