I'm not sure that's the right way to go about this. There are tons and tons of types of cheeses. I'm not sure you'll find a good list of all substitutes because it will be too big to put together.
Instead, I think you need to learn about the types of cheese so that you can make an informed decision. Is a cheese blue, sharp, creamy, hard, soft? How does it melt? What part of the world is it from? Those questions will allow you to find a cheese that is similar enough to make a good substitution.
For instance, if a recipe called for Pecorino a hard Italian cheese, Parmesan (another hard Italian cheese) would make a much better substitute than goat cheese or cheddar.
So see what cheeses are available at your local store. Write down the whole list (and preferably buy some of each). Get home and do a little bit of research on each one. Where is it from? How do people describe it? Take some notes on all of this. Then, when you see a new cheese in a recipe, look it up and see how it's described. Then find a cheese from a similar area with similar characteristics, and you should be good to go.
Edit: While I stand by my approach as a great way to go about this, I did find a good resource. Cook's Thesaurus has a great list of cheeses, including substitutes, broken down by type of cheese, type of milk, hardness, etc.
Best Answer
If I ignore the "on a spit" part I immediately think of Raclette, which is melted, roasted cheese served typically with bread or boiled potato.
In household settings the cheese is often heated in small individual pans under a table-top broiler, each guest gets his or her own pan and prepares his food.
Traditionally (and in larger settings) halved wheels of cheese are turned with the cut side towards a heat source and servings of molten cheese scratched off. The heating can be done either at a fireplace (embers) or on a special "machine" consisting of a heat source and a (often movable) tray for the cheese(s). The melting and serving is done by one cook for all participants. In Switzerland, but also sometimes in neighbourung countries, traditional Raclette is sold on food fairs, festivals and markets.