I also use the paper method. However, I live where summer and fall months are very arid with under 20% humidity on most afternoons. I cannot help but think that helps with this method.
Tomato seeds come right off the cutting board onto a paper towel or coffee filter. They will sit out on my deck under a roof for up to 3 weeks. Sunshine hits that location for a couple of hours every afternoon. The seeds and paper are stored in sandwich bags.
I haven't been doing this for 40+ years but about half that length of time . Germination success is very good for the first year or so. I have found that store-bought seed has as much variable germination and longevity as my saved seed. That seed is from multiple sources and that probably adds to my success or failure with it. Anyway, I try to be sure to have fresh seed by the fifth year if not sooner. That rule of thumb also came from experience.