I think it might be useful to analyze your situation by first looking at your basic Correll recipe. Sometimes a dough recipe will produce a crust whose characteristics (color, texture and flavor) are governed by the ingredients themselves and are not amenable to material modification in the oven during baking. When I look at the basic Correll recipe you referenced and see eggs, sugar, dried milk, water, salt, and oil, if I didn’t know better, and but for the high-protein flour, I would think I was looking at a yeasted cake recipe, not a pizza dough recipe. Maybe these ingredients will govern what you end up with more than any techniques you will use to bake the pizza.
Here’s the basic Correll recipe:
100%, Flour (medium-strength), 16 oz.
54%, Water (increase to 56-57% if high-gluten flour is used), 8.5 oz.
1%, ADY, 2 1/2 t. (Pete-zza note: 2 1/2 t. seems to be about 50% too high for ADY using the 1% figure)
8%, Sugar, 1.25 oz.
1%, Salt, 3/4 t.
4%, Non-fat dry milk, 0.625 oz.
2%, Egg yolk(s), 0.375 oz.
8%, Oil, 1.25 oz.
You indicated that you have been using two whole eggs and high-gluten flour. The high-gluten flour itself should provide better browning than a lower protein flour because of the higher levels of protein in high-gluten flour. According to Correll, if high-gluten flour is used, the hydration should be increased to 56-57%. This would increase the water content to 8.95-9.12 oz. As indicated in an earlier post, the amount of total water would then be reduced by the amount of water included in two eggs (versus egg yolks alone as specified in the recipe). I weighed two eggs (egg whites and yolks) this morning and got 3.1 oz (2 oz. for the egg whites and 1.10 oz. for the yolks). Since water constitutes about 85% of that weight, I estimate the final water weight to be around 6.5-6.7 oz. in the above recipe. Given that 56-57% is not particularly high for a high-gluten flour, you might consider raising the hydration to around 62-63% to produce a more porous dough and contribute to a more crispy crust.
The high levels of sugar (8%) and the use of non-fat dried milk (4%), along with the use of high-gluten flour as mentioned above, would ordinarily provide a substantial degree of crust browning all by themselves. However, using two whole eggs, which increases the baker’s percent for the eggs almost tenfold, from 2% to 19.4%, will mean even more browning. If anything, you may now be getting too much browning. And if the finished pizza browns too quickly, you might be inclined to take the pizza out of the oven before the crust burns. As a result, you may not get sufficient drying out of the crust to achieve the crispy condition you seek. Also, as previously noted in an earlier post, fresh eggs and crispiness do not go together particularly well.
I might also mention that high levels of sugar are often used in doughs with eggs to stabilize the eggs so that health issues (e.g., cross-contamination) don’t develop if the dough is kept at room temperature. Since the Correll recipe is one most likely intended for professional pizza operators rather than home pizza makers, I suspect that is the reason for the high sugar levels (more typical levels are 0-4%), since it is professional pizza operators who have to be concerned (because of regulations) about health issues like cross-contamination. In your case, I think you can safely eliminate a good part of the sugar in the Correll recipe. The eggs, dried milk powder and, to a degree, the high level of oil, should produce more than adequate browning, even for a same-day dough, and certainly for a retarded dough (because of the extraction of the natural sugars from the flours to contribute to finished crust browning).
Apart from browning concerns, the Correll recipe as you have modified it should produce a soft, sweet, and tender crust and crumb. This is because of the eggs (especially at 19.4%), the high levels of sugar (8%), the non-fat dried milk (4%), and particularly the high level of oil (8%). The low salt level (1%) will also serve to accelerate the rate and degree of fermentation, and with the relatively high level of yeast (at least 1% ADY), the dough should be able to rise pretty much without restriction and produce a good oven spring when used within a same-day or next-day time frame.
As I see it, unless you plan to change the recipe in some material way, especially as regards the use of eggs, sugar, water, etc., you may want to consider the following possibilities from the baking side: (1) Use a pizza screen, with or without par-baking the skin, and redeposit the par-baked/dressed pizza onto a 500-degree preheated pizza stone/tiles (the pizza can be baked at the middle oven rack position and the stone/tiles can be on the lowest oven rack position; (2) Bake the pizza on a screen, or on an oiled pan as you have been doing, remove it from the oven for about 10 minutes, and return the pizza to the oven for additional baking to (hopefully) crispen up the bottom of the crust; or (3) Use a lower bake temperature and a longer bake time, possibly in conjunction with the use of a pizza stone/tiles as mentioned above to achieve greater crust crisping.