Sorry if I am missing something, but I don't see the problem here. Most ovens have two racks.
Make sure that the gluten-free one is on the upper rack, so nothing from the other one can fall on it, and then cook both at the same time. You may need to allow an extra five minutes with both at the same time.
The problem was the lack of a microwave - I didn't mind sharing the oven, but didn't want to run the oven for an extra half hour (frozen meals take a long time in the oven, much longer than a frozen pizza) and cost my friend that energy for a small meal.