You can get Yupo and other reflective plastic supports and other transparent supports for coating. Less stable but good dyes are on the market and many are food dyes or clothing dyes. Pick three. The coatings are straightforward. You can make a reversal material. Endura type papers or C41 films, now that is hard!!! I've done both.
Of course it will not be Ilfochrome quality, but it will work. It will take dedication and a lot of hard work to get something usable. It may take years. But, it can be done. OTOH, as I said, C41 and RA4 materials are just about impossible for the home hobbyist.
A dye bleach solution can also be made to work with current materials with dedication and a lot of paper to burn, and a home brew coating will be usable but no Ilfochrome. In that case, you tailor your dye bleach solution to the new coating you are designing.