I just make the pizza on parchment paper on the counter, and then pick up the whole thing and transfer it, with the paper, to the pizza stone in the oven
This is an OK alternative to my peel-method posted below, but it can be tough not to let the toppings pile toward the center, since it tends to bow downward in the middle. I've done it before, it works alright.
I eventually settled on this too. My oven is a standard oven, not super hot, so we get enough heat through the paper from the stone before the top is done. But I do think a semi-deep cast iron pan pizza is ideal and foolproof for the home cook.