Oh, I know what you're talking about. I often work with two or more yarns in one project and keeping the skeins "free" is a major task :) Mostly I try to keep the skeins apart: one to my left, the other to my right. Fortunately I don't work with fuzzy yarn so I can untangle the yarns.
With doing this crochet in the round, couldn't you crochet around the end of the yarn you just cut? Like you do in tapestry crochet with the yarn you're not working with?