Cooking with a big paella pan on a gas stovetop

Hi everyone-
I have a big paella pan that I brought back from Spain that I love using. The problem is getting even heat distribution on my gas stovetop. I basically spend the 20 minutes of cooking time moving it back and forth, left and right, so the rice doesn't burn in four areas directly above the 4 flames, leaving the rest of the rice raw and uncooked.

Another wrinkle- I can't bake it because the oven is a typical Manhattan-apartment-sized standard small oven. Read: the pan won't fit.

Does anybody have any ideas of how to evenly distribute the heat on the stove so I can have perfect, hot, even cooking under my paella pan? i.e. buy a huge stone slate (like a pizza stone) to put over the burners to make one big flat heated surface. I'm not sure that would even heat enough to heat the pan and boil the liquid inside.

Ideas are welcome. Thanks in advance!