E6 has a higher load of developed silver than C41 but C41 has more restrainers so the bleaches are different and the fixes are different.
You can use the fix and bleach as long as they are not exhausted but I advise tests if you exchange the bleaces. The C41 bleach III is a new animal and I am not sure how it works with E6.
BTW, there is a comment elsewhere about Cellulose Nitrate films. I mentioned your PM.