What style of pizza are you making? The perfect Chicago pizza is different than the perfect NY-style pizza is slightly different again from the perfect Neopolitan pizza?
Since you mentioned the perfect pizza crust is thin and elastic, I'm assuming you mean an NY or Neopolitan style pizza, as the perfect Chicago-style pizza crust isn't all that thin. When you say pan, though, I think deep dish.
By elastic it sounds like you mean when rolling out. If that's the case, it sounds like your dough needs a bit of resting time before you roll it out to let the gluten relax after dumping it out of whatever container you are letting it rise in.
For an NY-style or Neopolitan pizza, you want to be baking at as high a temperature as possible. You ideally are doing this on a pizza stone, sliding dough in and out onto it. For these pizzas you want to be putting them on something hot. You only need to bake a pizza around 10 minutes, maybe even less, in a traditional oven at 550 degrees F (~ 278 C)
For Chicago style, I follow the most recent Cook's Illustrated recipe (from January of this year, not the older one that I definitely don't like) with a few adaptations to the crust (as, IMHO, the ideal Chicago style pizza crust is 80% bread flour, 12% semolina flour, and 8% rice flour by weight) and I bake at 425 degrees F (~ 218 C) with the rack in the lowest position of my oven for about 30 minutes.