Chewy Bechamel while making Moussaka
It may have been the mozzarella. When traditional Greek moussaka is topped with grated cheese, it is usually a harder, aged variety, such as Kefalotyri or Parmigiano-Reggiano. To thin the bechamel with additional milk, after the roux is complete, is fine. The roux should be very thick, as it's only flour and butter. It thins when the liquid is added, then thickens again as it simmers. However, if your bechamel was too thin and the cheese melted into it, that may account for the chewy result.