Avumede,
You might want to take a more structured approach to convert the Papa Del’s dough recipe to a deepdish stuffed format.
I will preface my comments by saying that I have never had a Papa Del’s pizza, and I have not attempted the Papa Del’s clone recipe. However, I understand that the Papa Del’s pizza is a very thickcrusted pizza and does not have a top layer.
To get a better grasp of the Papa Del’s clone recipe, I made an effort to convert it to baker’s percent format. In doing this, I assumed that the flour used is an allpurpose flour such as a General Mills allpurpose flour (the recipe itself is silent as to the type or brand of flour). I also assumed that the flour is measured out textbook style using the “stirliftlevel” method (stir the flour in the container, lift it into the measuring cup, and level off the top). Based on the above assumptions, I came up with the following formulation:
100%, Flour, 17.86 oz. (4 c.)
47.4117%, Milk, 8.47 oz. (1 c.)
2.80274%, Butter, 0.50 oz. (1 T.)
2.36273%, Sugar, 0.42 oz. (1 T.)
1.1026%, Salt, 0.20 oz. (1 t.)
1.40013%, IDY, 0.25 oz. (1 packet)
Total weight = 27.70 oz.
As noted in the above table, the total dough batch weight is 27.70 ounces. The Papa Del’s clone recipe says that that amount of dough is to be used with a 10” pan. The recipe does not specify the depth of the pan, so I will assume that it is 2” deep and that the pan is straightsided and, as the recipe instructs, the dough is pushed up to the top of the pan. Using the deepdish dough calculating tool at
http://www.pizzamaking.com/dd_calculator.html, and treating the milk as being equivalent to water for hydration purposes, I estimate that the thickness factor is 0.2074, as noted in the following formulation:
Flour (100%): Milk (47.4117%): IDY (1.40013%): Salt (1.1026%): Butter (2.80274%): Sugar (2.36273%): Total (155.0799%):
 506.23 g  17.86 oz  1.12 lbs 240.01 g  8.47 oz  0.53 lbs 7.09 g  0.25 oz  0.02 lbs  2.35 tsp  0.78 tbsp 5.58 g  0.2 oz  0.01 lbs  1 tsp  0.33 tbsp 14.19 g  0.5 oz  0.03 lbs  3 tsp  1 tbsp 11.96 g  0.42 oz  0.03 lbs  3 tsp  1 tbsp 785.06 g  27.69 oz  1.73 lbs  TF = 0.2074

By any definition, a thickness value of 0.2074 reflects a very thick dough. However, you indicated that you are using a 12” castiron pan and that you are using about onequarter of the dough for the top skin. If your 12” castiron pan is anything like my 12” castiron skillet, the top diameter is 12”, the bottom diameter is 10”, and the sides are 2” (measured on the slope). On this basis, and assuming again that the dough is pushed up to the top of the pan and that 25% of the dough is devoted to the top skin, I get the following from the deepdish dough calculating tool:
Flour (100%): Milk (47.4117%): IDY (1.40013%): Salt (1.1026%): Butter (2.80274%): Sugar (2.36273%): Total (155.0799%): Single Inner Ball: Single Outer Ball:
 506.45 g  17.86 oz  1.12 lbs 240.12 g  8.47 oz  0.53 lbs 7.09 g  0.25 oz  0.02 lbs  2.35 tsp  0.78 tbsp 5.58 g  0.2 oz  0.01 lbs  1 tsp  0.33 tbsp 14.19 g  0.5 oz  0.03 lbs  3 tsp  1 tbsp 11.97 g  0.42 oz  0.03 lbs  3 tsp  1 tbsp 785.41 g  27.7 oz  1.73 lbs  TF = 0.15943 628.33 g  22.16 oz  1.39 lbs 157.08 g  5.54 oz  0.35 lbs

As noted above, the thickness factor for the last scenario I described drops to 0.15943. That number still reflects a very thick crust. Also, as Loo mentioned, because of the nature of the ingredients used in the Papa Del’s clone recipe, it is likely that the crust will be breadlike as well as thick, which may make it difficult to avoid getting a fat lip. One way to deal with that problem may be to use an even lower thickness factor or, alternatively, leave the thickness factor at 0.15943 but use a smaller percent of the total dough batch for the top skin and hope that that results in a thinner lip when you join the top skin with the rest of the dough. Which option to choose may turn on whether you want a really thick crust or a thinner one. You may also decide that you don’t want to push the dough all the way up the sides of your castiron pan. I have given you all of the baker’s percents, so you should be able to use the deepdish dough calculating tool to enter whatever set of values you would like to cover your particular situation and desires. You might also decide to use a different flour, although doing so will change all of the numbers. It will also be possible once you settle on a particular set of values to convert the weights of the flour and milk back to volumes, using forum member November's massvolume conversion tool at
http://foodsim.toastguard.com/. If you need any assistance, let me know.
As far as the problem with the bubbling of the top crust is concerned, you might consider prebaking the top crust before putting the sauce and any other ingredients on top of the top crust. Given the breadlike character of the Papa Del’s clone dough, I don’t know how that will work out. But it is a method that is sometimes used.
Good luck.
Peter