What you are asking for is known in the trade as a short-time (or short-term) or "emergency" dough because of its very short lifespan. It is not a dough that I would use personally, beyond experimentation, because the finished crust will lack good crust texture, flavor and aroma. Also, unless a high protein, high-gluten flour is used, the crust coloration can be on the light side. It takes a long time (several hours at room temperature and several days for a cold fermented dough) for the biochemical activity in the dough to produce all of the above desired characteristics. Moreover, the crust will not be as readily digestible because the enzymes that will have to break down the protein and starches in the crust will be in your stomach, not in the dough itself.
However, if a short-time dough is what you want, there is a way to produce it but it will take more than just one hour. I am sure I could come up with a dough recipe that would allow you to make a pizza after a one-hour rise as you requested but it would take a lot of yeast and the finished crust would be almost completely devoid of color and taste. You would perhaps forever give up the idea of making your own pizzas after eating such a pizza and you will curse me up and down for leading you down that path.
Since a NY style pizza seems to pass your threshhold test, you might want to take a look at Replies 407 and 408 starting at http://www.pizzamaking.com/forum/index.php/topic,576.msg27251.html#msg27251
. If the pizzas described there are of interest I would use the strong white bread flour, and also the "Fast Acting Yeast" which I assume is the same as our domestic instant dry yeast (IDY). I would also modify the dough recipe to make a thinner crust. For two 12" pizzas, the following dough formulation that I put together using the expanded dough calculating tool at http://www.pizzamaking.com/expanded_calculator.html
might meet your requirements:
Olive Oil (1%):
|340.15 g | 12 oz | 0.75 lbs|
204.09 g | 7.2 oz | 0.45 lbs
2.38 g | 0.08 oz | 0.01 lbs | 0.79 tsp | 0.26 tbsp
5.95 g | 0.21 oz | 0.01 lbs | 1.07 tsp | 0.36 tbsp
3.4 g | 0.12 oz | 0.01 lbs | 0.76 tsp | 0.25 tbsp
555.97 g | 19.61 oz | 1.23 lbs | TF = 0.0867
277.99 g | 9.81 oz | 0.61 lbs
Note: Nominal thickness factor = 0.085; bowl residue compensation = 2%
You will note from the above dough formulation that I used a bowl residue compensation of 2%. That is to compensate for minor dough losses during the preparation of the dough. If you will be using hand kneading, you are bound to experience such losses because of dough that ends up sticking to the bowl, your mixing implements, your hands and your work surface. If you use any of the volume measurements given in the above table, you should round them out to the nearest measuring spoon sizes. The volume measurements are for U.S. measuring spoons.
If you decide to try the above recipe, you will want to be sure that the water you use is on the warm side, perhaps as high as 120 degrees F (about 49 degrees C), and possibly even a bit higher, to be sure that the finished dough temperature is in the range of about 85-90 degrees F (29-32 degrees C) so that it can rise more quickly than a normal dough. These figures assume a room temperature of about 70 degrees F (about 21 degrees C). If your room temperature where you are in the UK is higher or lower than that, you should adjust your water temperature accordingly. I suggest a digital instant-read thermometer to measure your temperatures.
The above formulation represents just one such formulation that can be used to make a short-time dough. There are several others on the forum. For example, another popular NY style short-time dough is the one described at http://www.pizzamaking.com/forum/index.php/topic,3736.msg31160.html#msg31160
. Also, if you go to Reply 25 in the same thread, at http://www.pizzamaking.com/forum/index.php/topic,3736.msg48427.html#msg48427
, you will find a compilation of several short-time dough recipes that I put together. I also saw another short-time dough recipe recently at http://www.pizzamaking.com/forum/index.php/topic,7405.msg63813.html#msg63813
As far as your oven is concerned, I think I would go with the main oven. If the maximum temperature that your oven can deliver is 450 degrees F (about 232 degrees C), that may mean that you will have to bake your pizza a bit longer. However, that temperature should work and it may even yield a somewhat darker crust. If the crust becomes too dry or chewy or crispy as a result, you may have to make an adjustment in the hydration of future doughs.
Good luck. I hope you will report back on your results.