Your last paragraph is critical in understanding what is going on or what might go on. Without the proper mordant, you can even lose dye from the print back into the second or third matrix as you are doing transfers. There are a number of things that can go wrong without mordants, but you have touched on some of them.
As for the rest of it, I think it important to know what is going on in the real, perfected dye transfer process marketed by Kodak. If you don't a lot of things may get lost over the years. But, much of this is covered in Jim Browning's web site and I cannot stress the importance of his information enough.