This is cute (and cool for the students), but I don't understand why the mushroom shape is important---it seems like the key innovation is the stem that extends past the watery stuff and deeper into the ketchup.
Good point. Perhaps the mushroom part is to keep the cap from slipping out?
In any case, this seems to be a solved problem. Fast-food restaurants already have ketchup pumps, with a very long stem that goes nearly to the bottom of the container. For home use, there are ketchup squeeze bottles that sit on their caps, so the watery stuff is on the opposite end of the bottle.
It appears that the real problem is that ketchup companies persist in selling ketchup in bottles that are not appropriate for ketchup -- and consumers keep buying them.