I think you are really onto something Nate, and Leo has some really helpful links and suggestions towards your goal. I will be trying to do something similar this summer during an internship. My goal is to produce some smaller squares of "wetland sod" for a stream restoration project. I just want to weigh in with a quick (because that's all I have time for now) comment or two.
I think making it 2-4 feet thick is way bulkier than necessary. Little or no soil is actually necessary unless you need to grow your plants on the "island" before it is floating (and you plan to water it often until it is floating!) You should mostly be concerned with creating a matrix in which the plants can anchor themselves and create a rhizome network throughout.
Speaking of anchoring...some kind of rigid frame, (whether sealed PVC pipe, bamboo, wood, whatever,) would probably need to be incorporated if you plan to tie it off somewhere. It may "anchor" itself by rooting if you leave it near shore when water levels drop.
I found this Baltimore project that used a Floating Islands International system (plastic matrix and foam floats) and also some handmade "Biohabitats" planters. Looking at the slide show linked below, these are only a few inches thick and stuffed with biochar. Substitute the plastic netting with plant fiber (coir, jute...), build maybe a more "natural" wood frame which you could lash together with a similar fiber, and stuff it with materials like Leo mentioned and I bet you'd have some measure of success.
http://www.biohabitats.com/projects/baltimore-healthy-harbor/Did I say "quick" comment? Oh, well. I hope this helps. I'm intrigued with the subject and will probably have more to add later. I probably should introduce myself on the forum, too...Next time!
