Cooking pizza in tiny gas oven with pizza stone
I realize this is an old question, but here goes. FWIW, I used to bake pizza w/gas, but for the last 15 yrs, it's been electric. Lots of variables, such as thickness of dough and baking stone, etc. but experiment with some of these tips:


Make sure baking stone is hot enough (I use an inexpensive laser remote thermometer).
Place stone on top rack. Heat rises and the roof of the oven will then emit enough heat to thoroughly cook the sauce and cheese. This will emulate a pizza oven. (And no need to par-bake crust.)
I usually crank up the temperature to 550F.
Slide the prepared pizza from a peel onto the stone (I use rice flour or parchment paper to prevent sticking). A peel could be an upside down cookie sheet, thin plywood, or even cardboard if you don't have a real peel.
Baking time should be around 5 min., and a little char on the bottom adds taste.
The above is based on NY-style pizza, but thicker crusts may need longer times--possibly at a lower temperature.
Good luck. The doorbell may be me. I'll bring the beer or wine.