I would just take your fish out and do it all at the same time. Unless you have a really wimpy filter or just cleaned it, then there should be more than enough in your filter. Be ready to do water changes, but from my experience if you keep the feedings light for a few days you don't need to do anything.
Doing it in portions stresses your fish like no other. If you insist on doing this method, I would do a very very thorough gravel vac to try to get rid of most of the mulm. Even then your water is probably going to turn out really dirty and maybe clog your filters...