I agree the Facebook message seems appropriate. I don't think you have to make it too long. "Hey guys, we're working on the TY notes for our wedding, and we have a few gifts whose givers we can't identify." If you've already sent the rest of your TY notes, you could leave unsaid what the gifts are, and just ask that people who haven't gotten a TY note from you message you about their gift. Or, you could specifically say, "There's a blue Kitchenaid mixer, a white toaster, and some brown bath towels." I'd start with two or three items and see if that shakes people loose--someone might tell you, "Hey, I gave you a set of kitchen utensils. I was second-guessing myself about whether the card would stay attached, so I wanted to let you know." And then that might take care of another mystery gift.
You could also circulate your question around your family/social circle--like designate a close friend or family member to investigate. Of course, they shouldn't be interrogating people about what they gave, but rather asking, "They got a blue Kitchenaid mixer--any idea who that might be from?"
I think it's good to make an effort, but if in the end you still have a couple gifts unaccounted for, there's no need to stress about it, IMO.