You might try dried powdered cheese. They have a few different types. Yes, it's been processed and the flavor isn't quite the same but I think it's better than the Velveeta answer. I've used it in cheese Grissini and similar to avoid the grease melt down.
http://www.spicesetc.com/ShowView/product/427/3
Hope the link works.
Helen Witty recommends this work-around if you can't get the cheese product I mentioned above. This has better flavor, but isn't quite as well behaved as the commercially dried product.
2 pounds natural cheddar cheese
Using a fine grater, reduce the cheese to the finest possible shreds. Strew the cheese over two or more baking sheets.
Oven method: Heat the oven to 130-140 for a convection oven. In a conventional oven, preheat it for a few minutes at its "keep warm" setting and turn it off. Leave the oven lihgt on to furnish gentle heat and turn it on briefly at "keep warm" from time to time; don't let any kind of oven get too hot. You can spread the drying into multiple sessions if you have other uses for the oven during this time.
Dry the cheese, turning it with a spatula once in a while until it is crumbly (and oily) which usually takes at least 6 hours.
Spread the cheese on paper towels and blut up as much of the fat as possible, using additional towels. If it has form clumps (likely) whirl it a food processor or blendcer until it is well pulverized. Stored in a tightly covered jar in the refrigerator it keeps indefinitely (Phil: probably not, but she uses it fast enough that she hasn't found the death point).
Using a food dehydrator. Put the cheese on solid trasy for drying fruit leathers and such. Keep the temp low, 110-115 is about right her machine. Dry the cheese until it is crumbly, stirring it occasionally. Blot the butterfat at intervals. Treat clumps as in the above method.
An off topic ramble:
Back in the 60s, I was dying to get my first set of Legos. Some were available if you mailed in two Velveeta box tops. I hounded my mom for weeks before she gave in. I think that was the only time we bought Velveeta besides for fish bait.
Now my kids play with those same Legos.
Phil