I can't speak for the neo-neapolitano and Reinhart foccacia recipes, but the basic Lehmann NY style recipe is a commercial recipe intended to be used by professional pizza operators. As such, one of the main purposes of the recipe is to produce dough balls that won't rise excessively while they are under refrigeration. Using small amounts of yeast and keeping the finished dough temperature around 80-85 degrees F (75-80 degrees F in a home refrigerator environment) will usually satisfy this objective. At the same time, the dough balls should last up to three days or more (even though most pizza operators tend to use a one-day window of usability). What is most important when using small amounts of yeast is that the finished dough temperature be in the abovementioned range. To accomplish this, we use a water temperature that will achieve a finished dough temperature in that range.
In your case, there are a few things that you can consider. One, you can use more yeast and warmer water such that your finished dough temperature is higher than the range mentioned above. This combination will speed up the rate of fermentation and result in a dough that rises faster, even while in the refrigerator. However, the useful life of the dough will be reduced, usually to about a day or so. Also, the crust flavors will not be nearly as pronounced as you will get by using less yeast and a longer fermentation time.
Two, you can try another dough recipe that is intended to produce results within a few hours, or up to several hours but not held overnight. These doughs are sometimes called "emergency" doughs or "short-term" doughs. To make these doughs, the usual practice is to substantially increase the amounts of yeast and use very warm water. The dough balls will rise very quickly and be usable within two to four hours. The downside is that, for most people, the finished crust will not have particularly good color, texture or taste. However, for some people, speed is more important. And there are people who actually prefer the pizzas made that way. It is essentially a matter of personal preference. I am aware of several pizza recipes that fall into the few-hours same-day category. If you would like a few links to those recipes, I'd be happy to provide them.
Three, you can use a combination of room temperature fermentation and cold fermentation. For example, after the dough has been made, it can be left to ferment at room temperature for a few hours and then refrigerated. This will cause the dough to be ready sooner. If you use enough yeast, you might even be able to use the dough the same day.
I think your yeast may be fine, especially if you have had no problems with the yeast with other kinds of yeasted baked goods. I have yeast that I have kept in my freezer for longer than six months and have not had any problems with it in any of my dough recipes. If you are using the three-strip packets of yeast and they are sealed, I think they may still be OK if you refrigerated them rather than freezing them. Otherwise, I would buy a fresh supply to be on the safe side. You can also "proof" the yeast. The way to do this for ADY is described here: http://www.breadworld.com/FAQ.aspx