I agree with Wayfaring Stranger, this plant is slow to grow after transplanting because it is one of those plants that likes being 'root bound'. I would transplant this guy again in a slightly larger clay pot. Firm the soil around the roots in the pot and leave an inch below the rim and the top of the soil. The clay pot won't give like the plastic one and will contain those vigorous, large roots much better. This next transplanting I would get a big chunk of panty hose to put over the hole before you put your soil and plant in the pot.
When there is more room in a pot with more soil, this type of plant will first fill that soil with roots before working on more top growth. You just transplanted it and already it has filled the pot with roots and now checking out the 'mud room'. That thin light plastic pot will easily be deformed and unless you put a very permeable barrier over the drain hole those roots will continue to grow and tip your pot over.
You could just leave it right where it is, chop off the roots as they come out of the hole. Will not hurt that plant. Press the soil down and I think you'll be able to get a 1" space from the rim for watering purposes. The top growth should begin again soon. When it gets going and outgrows this pot (top growth will slow again) then get a heavy clay pot that is no more than 2" larger in diameter.
There is nothing wrong with your plant at all. And I changed my mind, I wouldn't transplant again right now. Chop roots off or poke them back up in the hole. Allow your ZZ to grow more top growth first to feed and support all those roots. It loves being root bound. It should start showing top growth soon.