I used to do the Clark Flush with epsom salts. Now I do the coke flush because I find it much easier to drink. I always understood the purpose of the epsom salts was to open the bile duct - same as the ultraphos - as well as to empty the colon. So, if I feel that I haven't had as much ultraphos as I should have, sometimes I take a shot of epsom salts 2 hours before the flush to make doubly sure the bile duct is open wide, but I don't always do that.
As far as the colon being cleaned out, I usually take oxypowder to clean that out about 3 hours before the flush and sometimes I take it the night before as well. (It might dissolve some of my last meal before it gets digested but I figure that's not a big issue.) It'll be different for different people, but usually I get a lot of brown water about 5-8 hours after the flush with all the stones and scum and stuff floating on the top. So the stones aren't stuck and getting reabsorbed. But I've never tried it without epsom salts AND without oxypowder. But you say you're using Oxypowder now, that should be all you need.
There's really a lot of leeway for mucking about with the basic recipe. I suspect that all you really need to do is drink 4 ounces of olive oil. (I remember a newspaper article about a healthy 120-year old woman in the Middle East that said she drank a glass of olive oil every night before bed, you can still google it -- I said OMG, she's doing daily liver flushes.) The rest is all to open the bile duct to ensure that it's painless, and to clean out the colon so that you can SEE what's coming out. (For the people that don't do that, I've heard that many people sit on a colander and rinse it to see what stones are left after the rinse.) And some people will get a colonic the next day to make sure they're all cleaned out but that's expensive.