I have used basically the same bleach formula for both C-41 and E-6 for quite a long time. However, I am using scratch-mix not-official bleach and fixer formulae, and the principal difference between the two relates to dye stability and color balance, but perhaps PE is willing to contribute more information to the discussion. I would appreciate hearing an historical perspective of bleach formulae.
I also use and prefer a quinone-persulfate bleach that is clean-working and more economical to mix. I have films of various manufacturers, both C-41 and E-6, processed over the past 25 years or so that are to my view much the same as when processed. I understand there are stability issues and that the official chemistry is formulated carefully to yield consistent results, but I have nevertheless been happy with my results on both counts. It is also my understanding that the current Fe-EDTA bleach formulae were made more for environmental reasons than for optimal photographic chemistry.
Color balance varies a little with different bleaches but even a simple copper-chloride bleach works well enough to produce C-41 negatives that balance well for either printing or scanning. Who knows about the stability of color dyes bleached that way? My oldest copper-bleach test films are around twenty years old and these appear ok today. I went to scratch mixing a long time ago when chemical cost was a bigger factor for me. Now I prefer to mix my own chemistry mostly to have solutions available on demand without having to order and pay onerous hazmat fines. I settled on the quinone-persulfate formula because the chemical cost is less and it avoids the need to ship Fe-EDTA in liquid form. The Fe-EDTA sulfate (solid form) is increasingly difficult to locate and both forms tend to be pricey.
My films are stored in archival or glassine sleeves in 3-ring binders on the shelf at normal room temperature.
I suggest you try some of your own experiments to see if you get a result that is satisfactory for your purposes. If you PM to me I am happy to send you the formulae I am using.