Not all cheese is created equal. Pre-shredded cheese is a trap. It’s coated in cellulose (wood pulp) to stop clumping. That wood pulp blocks melting. It makes your sauce gritty and dry. Grate your own cheese. I know it’s annoying. Do it anyway.
Use a mix: sharp cheddar for flavor, Gruyère or Monterey Jack for meltability. American cheese slices (the real ones) are okay. They’re engineered to stay creamy. Just don’t skip the bit of cream cheese or a dollop of crème fraîche. It adds acid and stability.