Personally I'm not sure reducing the number of TDs would increase participation, for me it's kind of a multi-headed issue.
First I'm just not that creative enough to come up with things that fit into the categories, so I often don't participate based on not coming up with a good idea. Second, the people in my house are all really picky eaters so if I do happen to come with something I'm usually just making it for myself, which kind of takes the fun out of it for me. And finally, and this is the big one, having time to plan, prep and execute a TD is not always easy to come by around here. Between, school, sports, scouts, camping trips, dealing with family etc. having time do dedicate to a TD entry, especially when it's just me eating it, is not something that happens very often.
Anyway, all that said I have no idea how any of that helps you increase participation, but I think reducing the opportunities would hurt my ability to enter even more. Maybe if it were 2 TDs per month, offset by a couple weeks and make them go a month each? I dunno. The month long TDs are easier for me to enter since I can do a bit of prep here and there, and then plan a day to actually do the cook.
I do like the idea of a Tournament of Champions type TD for the previous years' winners, or something along those lines.