I feel like I am shooting down ideas, and I don't mean to, I really appreciate them!
We tried a White Elephant gift one year (in addition to the regular exchange) and it did not go over well. Most of us already have to do one at work and some of us with in-laws as well and it was just too much of it.
A general swap type gift doesn't really work well for us as we are very very different, most of the things I would love, my sister-in-law and brother would HATE with a passion and food/drink type gift would be hard as we have several alcoholics (some in recovery, some notsomuch) and the non-alcoholics love weird beers etc. Most are very good cooks, plus 1 doesn't eat meat and another is constantly concerned about the calories in everything.
The bigger reason why a general gift would not work is the same reason I feel guilty that it is not happening this year: for the quiet 2, this is one of the very few gifts they get for the holidays. While many of us have spouses and other family members who buy for us, for some this is their "big" gift for Christmas and I like to make it something very nice and personal (the exchange gift was usually ~$40). I am buying for them this year as well just because, but because there is no exchange they feel guilty about it. I just love to search for the perfect item for people, and the best solution may very well be for me to just suck it up and ignore the frustrating parts of the exchange.
I just wish I could get brother1 to understand that with 10 people in the exchange, 2 he cannot have (himself and his wife) and 3 others he doesn't want, it IS going to happen every other year or so!! Maybe my gift to the family is to tolarate his complaining.