Lol, I don't have chickens, but I do have "cat time". We have 7 cats, 2 upstairs (my husband mostly cares for those) and 5 downstairs as well as a small dog (I care for those) and when I go downstairs to take care of the animals sometimes I'm down there for quite some time.
There are 5 litterboxes and the dog isn't housebroken so he lives in a pen in the basement (to contain his mess) that also needs to be maintained so it can take a while. I've got a pretty good system with the litter boxes now so they don't take forever to clean when I clean them (I don't do all of them every day, I clean as needed, 2 of the boxes get cleaned every day, the other 3 are closer to once a week when they need to be cleaned). The dog cage.. It's gross, it gets cleaned about once a week right now because it's an ordeal to clean, he's on pine pellets and they have to either all be thrown out or sifted.... I'm getting ready to change his cage up some and see if that helps any.
Like you, I have critters that have to have attention while I'm trying to clean, most of the time I'm cleaning a litterbox with 1 hand and scratching a cat with the other, the cats rotate in as to who I'm scratching when and the dog gets into the mix as well...