Sauce – I would like to know how to thicken sauces with blood and is it safe

I can give you the Italian answer - first of all, normally we don't use tomato paste to make sauce, but rather to add a tomato "kick" to recipes. Tomato paste is simply tomato puree that has been cooked down to a high degree of concentration.

A basic tomato sauce is made by

1. making a soffritto with onion, carrot and celery (plus other flavors)
2. adding tomato puree, or "pelati", more rarely fresh tomato
3. cooking the sauce down until the taste and thickness is what you want

If you want to use paste instead of puree, the third step has to be omitted or greatly reduced in duration. Keep in mind that tomato paste has its own taste, and that taste will remain in the final sauce.

Why not make a thick cream sauce, like an Alfredo or some such?

It's basically some cream with some white wine and maybe a little flour. You can add some parmesan to it, if you want it a little thicker and yellower.

I'm not sure what would happen if you beat an egg into it as well, but it might be worth a chance.

I'd also consider using beetroot for the filling. It has a very satisfying red colour, and it's a little sweet in itself, which should go well.