If I'm reheating things in tins and I don't have enough oven space, can I stack them on top of each other?
As long as the containers can support eachother, it is likely safe to stack them. You biggest issue will be uneven reheating. Containers at the center are likely to remain cold. If you do stack them, insure that you occasionally rotate them. If possible, try to stack them in a way that allows for air flow around them. Stack layers at 90 degree angles.

The flash point of paper is about 450F so you should be fine with the covers.