JD - I'd be inclined to try with only about 100ml water and cook everything except the pasta and egg for 10 minutes, then add the pasta and cook for 3 minutes and then add the egg and mix without heat - just gently mix it thru on reverse and let the heat in the mix to cook the egg.You can add some water if it looks too thick.
You are a champion JD - I worry that I may kill somebody with my suggestions. Hope MM has good insurance