Yes, I would be required to make and keep them at market. For right now to experiment with using a starter, I would just use a starter I have here at home and give samples to standholders to first see if a natural starter would work to improve the flavor of the crust. There are many standholders and workers at market that purchase my pizza. I would let them know that I made the starter at home. They wouldn't mind if I used them as guinea pigs. They have know me for years. I still have a food approved shed here at home that we used to pop the popcorn and make candy in. I also could use that to make the starter, here at home.
As for starting a natural starter at market and maintaining it, that might be able to be worked out. I don't live that far from market and could go there until my starter is active and then refrigerate it, until needed. I have a disc heater that I could use to warm up the starter, that was refrigerated.
If you think this is not an option or would present too many problems, let me know. Do you think the temperature would be too cool to activate the starter at market.
As I see it, the biggest issue is one of logistics, especially trying to adapt a natural preferment version of the Lehmann dough formulation to the somewhat unpredictable temperature environment of the market where you would be making your doughs. As we previously learned, the widely varying ambient temperatures of the market where you have been making your pizzas pretty much ruled out a room-temperature fermented biga and, most likely, any other preferment, natural or otherwise, that would rely on prefermentation at room temperature. In a way, that is a shame because I believe that natural preferments work better at room temperatures than in typical cold fermentation applications of a day or a few days and, as a result, yield more complex crust flavors and textures. I discovered this in one of my early natural preferment versions of the Lehmann dough formulation, which I described at Reply 151 at http://www.pizzamaking.com/forum/index.php/topic,576.msg11774.html#msg11774
. These days, I would use the preferment dough calculating tool at http://www.pizzamaking.com/preferment_calculator.html
to come up with a better and more accurate set of numbers. Back then, I was in the preferment learning stage and knew a lot less than what I believe I now know (I have also learned more about autolyse).
But, even if a spruced up version of the dough formulation described in Reply 151 might apply to your situation today, you are still left with the need to make and manage a quantity of natural preferment for a commercial batch of dough. I looked at some of the early Lehmann dough formulations you posted and that I believe you were using and it seems to me that you don't need a very large quantity of natural preferment to make your doughs. However, you would perhaps need a unit like the ThermoKool MR-132, or something equivalent, to control the temperature of the natural preferment. I don't think you can manage a natural preferment in a widely varying room temperature environment and get consistent, reproducible results, although you will be able to use your deli case to store the starter culture between feedings. But, even with a temperature controlled unit or facillity of some sort, you will still have to determine how to manage the natural starter culture and preferment for use in making pizzas only one day a week. If you have several starters and are feeding them regularly, I think that you will discover that you can go through a lot of flour just feeding and maintaining the starters. If you were a baker or artisan pizza maker making doughs throughout the work week, you would be using most of that flour to make dough.
You might take a look at what I discussed in Reply 151 referenced above to see if it is a possible candidate for what you would like to do. For additional insights and ideas, you might also look at what Jeff Varasano did with his Patsy's New York style clone at http://slice.seriouseats.com/jvpizza/
. My recollection is that Jeff originally used about 40% natural preferment as a percentage of the total formula flour but later significantly reduced it to around 9%. Jeff also used a small amount (0.25%) of IDY. I found that using a combination of natural preferment and commercial yeast resulted in less crust flavor but perhaps helped with oven spring. You might also look at Terry Deane's work with natural preferments (supplemented with 0.15% IDY) starting at Reply 25 at http://www.pizzamaking.com/forum/index.php/topic,7561.msg65261.html#msg65261
. I don't recall whether Terry went to using only a natural preferment, as he indicated he planned to do, but I am sure that he would have been able to accomplish making a dough leavened only with wild yeast. No doubt, there are other members who have worked with natural starters/preferments for cold fermentation applications and might be able to offer some advice to you for your particular situation.
If you end up using the preferment dough calculating tool, you will perhaps want to know that you will have to specify the percentage of water used in your natural preferment. That is a function of how much flour and water you use, by weight, in your regular feedings of your starter culture. If that number is not quite accurate, you may find that you have to adjust the water and/or flour in the final mix to get the proper finished dough condition.