Look at CJD (Creutzfeldt-Jakob Disease) or BSE (Bovine Spongiform Encephalopathy) the causative agent is a prion. A vital protein that in its normal state is essential to neurological function, which can fold in more that one way, and folded the wrong way destroys brain tissue and ultimately causes dementia and death. I'll bet dollars to donuts, that there is some funny quantum state, or a protein folding problem, or some simple nonbiological chemical process whose probable result is a code misspelling in protein formation. Its an interesting problem, but not at all surprising. We are complex systems, and trying to force the world processes that make us possible into a box is at once myopic and foolish.
Species like rabbits are resistant to prion infections and comparison of the crystal structures of prion protein in rabbits and in hamsters reveals why rabbits cannot get infected while hamsters can - its solely a protein folding problem.
The hard part is differentiating them into the tissue that you want -- safely.
I bet epigenetics and cell memory will have a crucial role here. Genome wide studies showed that many PcG and TrxG genes change their expression levels during differentiation. Also, i find idea of bivalent chromatin to be very attractive - a cell has histone marks that can either silence or activate genes and depending on the context it will be tilted hopefully the "correct" way.
The tumor evolves and all that our treatments do, if they are unable to kill off the entire tumor, is select for cells that are resistant. I'm not an oncologist, although I am involved in medical research, but it seems to me that a more effective strategy would be to select for cells that are specifically weak to conventional treatment prior to administering it.
You are touching on a cancer stem cell theory. There are many labs that work on that and a number of papers demonstrated experiments supporting the theory, at least for a couple of cancer types. And as you said, the best treatment (and possibly cure) for cancer is considered to be a combination therapy: an agent that kills off cancer stem cells (does not exist yet) + chemo/radiation therapy to kill bulk of the cancer cells (variety available and work fine, albeit with considerable side effects). The problem with getting an agent to kill off those CSC is that there is limited info about the molecular and surface markers, genetic makeup, epigenetic regulation of those cells. Once we (as in researchers involved in medical oncology) have pinpointed those, hopefully an effective agent can be designed.
If you're not part of the solution, you're part of the precipitate.