Mike, I've done this in the past. Same drill Ektalure, F5 two bath ,I usually would rinse off the fix, maybe 30 seconds , then into KRST. No staining because there was no unfixed silver left in the paper. I've tried going directly into KRST after 1 minute in Ilford Rapid fix 1+4, I got stains. I figured (right or wrong ) that the Ilford method of going into a wash before toning gave the residual Ilford fixer enough time to convert the extra silver halides in the print??? When I followed the Ilford method I got nice prints until I had prints stick to my drier belt.
I made hundreds of prints 30 years back following the procedure you spelled out above. They still look great. I think my problem with sticking, came from trying to mix old and new . Who dries prints with a belt dryer these days other than me? ? The ammonium thiosulfate revolution, and unfounded fears of hardener ruining your toning, spelled the end for F5 and other powdered Na thiosulfate fixers.
I'm going to make a 10 foot long tray rocker, then I will sit back and spend eternity fixing, clearing, toning and washing prints
There's a lot of ways to make great prints. Best Regards (the other Iowa ) Mike