I'm not a grilled cheese conneseur, but I can say the best cheese I've ever had is cave-aged Gruyère AOP Reserve, aged for at least 15 months, making it sharper than younger, more common gruyeres. Due to it's small quantity and expense, it is not distributed outside Switzerland. Why is it so good? It's from mountain cows freely graizing in the swiss alps (or rolling hills of west Switzerland), and much of the wonderfully clean mountain watered grass consumed there is also full of flowers (petals and sweet pollen), making the milk both sweet and floral. (I can also say what americans call "swiss cheese" is so far from the Emmentaler cheese it is trying to emulate, it is just a joke.)
Second to true swiss Gruyere, I'd say CABOT Vermont Extra Sharp Cheddar and/or CABOT Vermont Alpine Cheddar are the next best I've ever had.
If I were to make a grilled cheese, I'd look to these.
I would love to try this stuff someday. I think I can get some real (?) Vermont cheddar around here, but even basic-ass Gruyere is too expensive for my pleb budget.
Havarti+Muenster is still my fav combo.
That sounds like such a great combination! Muenster is so versatile, I used to get it a lot at this Polish deli near me when I lived in Chicago. They also had like a zillion different kinds of smoked sausage <3