I was picturing something like what Terrie posted, and what JDeluka mentioned, more like I envisioned Luann's original description. We each put our requested theme (spring, or ocean, or traditional blocks, or scrappy, or whatever), and then each month we make one row for whichever person is on our list.
We make something that fits that theme, in whatever manner we are comfortable with. So, for ex, if I want to make all log cabin blocks into rows, I would do that in a color scheme to match each person's stated theme. Or if I love appliqués, I would make some kind of appliqué row for the theme for that person. Either by making one long strip of 6" x 40" (or whatever length we say), or by making six 6" squares and joining them to a row, or whatever. If I prefer miniatures, maybe I would make all my rows out of miniature blocks. Or maybe I like variety, so what I make would depend entirely on whatever my recipient wanted....(this will likely be me).
I think too many rules to what is made might take the fun out, but perhaps we could have a list of rotating blocks and if the recipient prefers that version, she can put "traditional" as her theme, and we know to follow that list for her.
That might look like Jan -- log cabin, Feb -- 9 patch, Mar -- star block, April -- drunkard path, May -- churn dash, etc... And anyone wanting their quilt to follow that would mark "traditional" (probably include a color scheme), and anyone who didn't care could say "ocean theme" or "flowers" or whatever, and then people could have some freedom to do one or the other. I think the open people should be open to recieving traditional, if that is what their maker is most comfortable making, though, perhaps. Like in the example Terrie posted, some of the rows were free form, but some were traditional blocks.
Mostly I want something that ends up reflecting not just my personality (via my designated theme) but also representing each of the participants (via whatever row technique they use to make the rows). Make sense?