Have you tried Maggi sweet & spicy? It’s a fairly spicy sweet ketchup-y sauce. Fantastic with anything, but especially grilled cheese and (I hate to say it) mac & cheese.
Speaking of which … I don’t dip my grilled cheese in ketchup, but I do spread peanut butter on top of my sammiches. Absolutely delish. My wife and kids look at me like I have three heads, but I don’t care … more peanut butter and grilled cheese for me!
I learned that trick here on the boards a few years ago. It works exactly as advertised, and that’s how I’ve made my grilled cheese sandwiches ever since.
As for ketchup, no. I generally don’t take my grilled cheese with anything, but mustard is a better match for my tastes. For me, mustard + cheese are a natural pairing. And I hate tomato slices in my grilled cheese, too. (I love tomatoes in all their incarnations, but they completely mess up the experience for me in a grilled cheese sandwich.)