But a few cheeseburgers at a fast food joint costs $7.
If you're making it regularly, each bag of cheese at $4 isn't that bad. That might mean with everything told, you can make 5 batches at $3 each. Feeding 4 people on $3 isn't expensive to me. If you really want to save, buy the bulk blocks, 5 pounds of each cheese for $20-ish depending.
If you can't get that kind of scope and want to see the light bill for the one batch, have the deli cut you just a 1/4lb of each type, although that might well cost about the same as the bag of pre-shreded.