The utility sink, I have an older model front loader and I love it. 4 months ago the Router guy was here I had a jam from the kitchen garbage disposal didn't know on a well you don't use them. He noticed that all the garbage from the washer machine was dumping into the sink, I have dogs so a lot of dog hair. Then its the normal lint and crap. He suggested one product and clueless and said to tie up pantyhose. OK..few months later I am buying them because I won't! So, what do I put on this hose to catch the crap.Other than me buying stock in the eggs again!
I did notice that it drains better and I no longer have that mildew smell when you leave a front loader off for a few days.
I have the same set up as you, and I put this metal mesh screen type of lint trap on the discharge hose. It collects all the hair and any large debris from clogging the trap on the utility sink. It gets relaced every 3 months or so. You should be able to get it at any supermarket in the laundry isle. It looks like this: