Also I'm pretty sure the unconsumed cloudy particles end up being skimmed pretty quickly

I rinse my food but not necessarily to avoid adding phosphates to my tank. I also prefer putting in clean food because the cloudiness just looks untidy and I like watching my tank as the fish and coral are feeding. I use a tea-sieve that is very fine mesh so I still retain most of the food particles but just lose the milky colored water that it defrosts in.

I rinse with tap water (in a reusable coffee filter) whenever I feed the mysis. If I don't the residue that thaws out will make my skimmer go berserk!

I've also found that with my Deltec skimmer. If I neglect to rinse as soon as I dump in the mysis it suddenly starts bubbling like mad. What brand of skimmer do you use?

Bubble Magus

I rince with RO/DI water. If I don't I eventually get cyano build up again. Also after I rince the frozzen food I portion it as well into small cubes so I feed the same portions all the time. This makes it easier for the people who help me with my tank.