Since you don't want to use mods I would suggest that you get rid of the ice cream maker for a start. Unless you mod out the obsessive making and eating of ice cream you are stuck with it.
I don't use the deep fryer so am unaware of the invisibility glitch so I have no suggestions there. I vaguely remember using it a long while ago and that my sims kept trying to fry food autonomously so I stopped using it. I believe I have since downloaded a mod but don't like my sims eating fried food in any case.
Perhaps your sims would be more likely to clean dirty counters, etc. once you get rid of items like the ice cream maker or other premium items that sims obsessively use. I know my sims are always cleaning on their own and I never use the neat trait. I often have several sims converging on one dirty counter or to empty the potty chair.
Sims on high free will don't always behave as we would like. If your sim walking around in his tighty whities bothers you that much, direct him to change outfit.