if you're making your own - and you've got time so why aren't you ?
I like to use different types of pesto as a base instead of a tomato sauce.
lidl does three different types for a few pence a jar.
Keeps quite well and just stops all pizzas tasting of tomato puree
I've seen the egg ones, not yet tried it. I tend to make my crust fairly thick and fluffy so cook for about 20 mins - an egg would be hard as a bullet by the end. So not actually tried it.
If you're going for the 5 minute blast furnace variety, eggyolk should still be runny. That would work really well.
Cheese wise I use low fat mature cheddar.
Has all the stringiness of of mozzarella but plenty of flavour as well. I just don't see the point of mozzarella