Funny you should bring this up again, as I was thinking of deleting some information and pictures of this that I tried a month or so ago. I just quickly experimented at making a Barnaby's Clone pizza based on much of your initial thinking's and some more on what I thought may be in the dough ingredients (just doing some "guessings"). I had mixed results.
I generally stay away from volume recipes as was given, but figured this wouldn't be difficult, only I wasn't certain what size pizza this recipe would give me as no size or diameter was given. But I use a 14" cutter pan and it can accommodate any size up to that and that would be worth trying, I figured. Much, much prefer weights over volume as that way I can in seconds convert from one size to another very easily. And in so many ways, weights are much easier. But whatever.
The formula variation that I settled on for the Barnaby's Clone -- which just reflected some "guessing" on the flour blend component of the crust on my part -- was as follows:
9 oz. Flour Blend*
1/4 cup oil (half vegetable, half OO)
1/2 tsp proofed ADY
1/2 tsp sugar
1 tsp salt
1/8 tsp of NFDM
1/2 cup cold water (minus a shot glass full of water warmed to 105 degrees F to proof the ADY for 10 min.)
* The Flour Blend I settled on was a combination of a number of things that I thought may possibly be in the crust recipe. It consisted of 4.5 oz. of KAAP, 1.5 oz. of Semolina, 1.5 oz. of corn flour, and 1.5 oz. of corn meal (med. grind). The dough ball weight after all ingredients added and after several rises was 413 grams or 14.6 oz. if I remember correctly and if my notes are accurate from back then.
I mixed all the dry ingredients first with a wooden spoon, then added the proofed ADY yeast (much less than yours), then the remainder of the cold water (except for the yeast, I think cold water is better), then the oil and mixed all together by hand for 5 or so minutes. It went together nicely, slightly oily, but not too much. I rolled it into a ball, covered the bowl with Glad wrap, and put it in a very slightly warmed oven for about an hour, then rerolled the ball, then in another hour repeated the same, then on the countertop for a number of hours and into the refrigerator for a day or so., etc. With a half tsp of "proofed" ADY, this dough rose and rose and rose nicely. I can't imagine what 2 to 4 tsps of yeast would do to the dough! (Parenthetically, I'm puzzled by your phrase "and the dough goes flat" because with my half tsp of proofed yeast, it could never go flat within a day or so.)
The dough ball handled ever so nicely and it proofed up several times ever so beautifically that made me very optimistic about the outcome. I rolled the dough out to fit my 14" cutter pan and pinched up the edges of the pizza rim accordingly, dressed the pizza with some Glen Muir pizza sauce, pinches of uncooked Italian sausage (almost the only way to go with a Barnaby's pizza), cheeses and oregano/basil spice sprinklings and ready for the 450 degree F oven for . . . much, much longer than I thought (guess it was 20 to 28 minutes).