How can I achieve a good socarrat with paella cooked in the oven? I'm cooking dinner for a friend who pointedly bought me a paella pan. Normally, I would never consider making paella in the oven, but my stove is electric and the coil is not nearly as big as the base of the pan. So I looked around and found this recipe from Bobby Flay.

I just made a test batch with just the sofrito and rice. Since the recipe didn't mention the socarrat, I figured I'd be slick by preheating my pizza stone at 500F and placing my paella pan on that. It didn't work for creating the socarrat, but other than that, I was mostly pleased with the results.

So, I'm pretty married to the technique in the recipe, but I'd still like to get that crusty rice layer on the bottom. I tried putting the pan on the burner for a few minutes after the rice was done, but that just gave me a burnt bottom layer.

Any ideas?
Putting the pan on the burner will deliver too much heat in too little time - aka a burnt layer.

You want constant heat from the bottom during the whole cooking time. In an oven, your pizza stone is an excellent start, supplying a thermal mass. I recommend increasing the heat from the bottom compared to the heat from the top, even if this could slightly increase the total cooking time:
Set your oven to "bottom heat" and / or put the pan on the lowest rack possible. A sheet of foil can also shield the pan from top heat.