You know those lay flat tackle boxes with all the compartments? We took out the dividers and each kid had their own cubby. NO chance of touching, you could put the toothpaste on early and they were easy clean. We drilled holes in the boxes and tossed the whole thing in the dishwasher.
you can buy a expensive, big one on amazon, It gives you a idea at least of how to create a cheap walmart version
https://www.amazon.com/Preventive-De.../dp/B0042SSVIE