I hope that Joshua won't mind if I contribute some pictures of a bill fold I learned. It's not really origami, I guess, but I didn't want to start a new thread since this isn't really a collectable bill. I learned it as the "Braided Bill" fold, using a book and video by Robert Neale.
Here it is:


The interlaced bill is created with only 2 internal slits (this is the practice bill I used to learn to weave and unweave the strands):

It's a 3-step series of folds/interlacings; the first 2 steps are very easy, and the last step is so complex it never really got explained in the materials I studied. The first time I made it work, I had to stop and say, "What did I just do? Can I ever do it again?". (After a while, I could...)
Apparently there are some similar interlaces used in leatherwork.
I hope you find it interesting!