From what you have said, I believe that your main problem was the use of too much water in the dough. This can easily happen when you are using volume measurements and have not yet developed the proper technique for preparing the dough. You will get much better with experience, I can assure you.
I will also mention that the two Reinhart recipes you mentioned are prone to the types of problems you experienced. I recently made Peter Reinhart's NY style dough and the recipe is similar to the two you mentioned. All three recipes call for the use of fair amounts of yeast, sugar (and/or honey), oil, and water. I estimate that the hydration ratio of the three recipes, that is, the ratio of the weight of water to the weight of flour, is around 62.4%. That, in itself, will produce a dough that will ferment (rise) fairly quickly and spread out within its container, even in the refrigerator. With high levels of sugar and oil also, that result is virtually guaranteed. Also, the use of the 5 minute rest period during the dough mixing/kneading cycle and the 15-minute rest period before refrigerating the dough will cause the dough to warm up and ferment (rise) faster. I suggest that next time you try the recipe, use a larger storage bag so that there is plenty of room for the dough to expand and spread out. Even if the dough is fairly soft when you are ready to use it you can at least get your hand under the dough and gently remove it from the storage bag without having to destroy the bag to get the dough out. If you go to http://www.pizzamaking.com/forum/index.php/topic,524.100.html
, where I discussed my results from using the Reinhart NY style dough recipe, I think you will identify with some of the characteristics of the dough I described at that post. The difference is is that I have more experience in dough management than you do. But you will catch up soon enough.
Now, back to the dough wetness problem. Terms like "wet" and "dry" are necessarily relative terms. I tend to prefer the use of the term "tacky" because people can better relate to that term if they have ever touched drying paint. "Tacky" also falls between wet and dry by any definition. Once you learn how to make dough properly, the terms will diminish in importance. You will know by touch and feel and you will wonder what the fuss was all about. For now, I would suggest that the next time you make the Reinhart dough you use the following approach. Start by putting most of the water in your mixer bowl, reserving about a quarter of a cup. Add the salt and sugar (or honey) to the water in the mixer bowl and stir to dissolve. Combine the flour and instant dry yeast, set the mixer at stir or 1 speed, and add the flour/yeast mixture slowly to the mixer bowl. If necessary, use a spatula to help deflect the flour/yeast mixture in the direction of the dough hook. I have learned how to do this while the mixer is running but if you feel more comfortable stopping the mixer to do this, that's not a problem. And don't worry about messing up the elapsed times. Most times recited in recipes are usually wrong anyway. Continue adding the flour/yeast mixture to the mixer bowl until a rough dough mass is achieved. I don't usually use a rest period in my doughs, but if you would like to be true to the Reinhart recipe, then introduce a 5-minute rest period. It will help increase the hydration of the dough (the absorption of the water by the flour).
After the rest period, if you use one, add the rest of the flour/yeast mixture, add the oil slowly to the mixer bowl and run at 1 speed for about a couple of minutes, or until it looks like the oil has been taken up completely by the dough. It is at this stage that you want to test the dough to see if it needs more water. If the dough looks and feels really dry, then add some of the reserved water, a teaspoon or tablespoon at a time, and observe the changes as the added water is mixed in. You can use the 1 or 2 speed of the mixer. You will usually not have to add more flour since you have held back part of the water to intentionally keep the dough on the dry side. However, if you overshoot the mark with the added water, you can safely add a bit more flour. At some point, usually after about 4 or 5 minutes, the dough just won't take any more water without becoming obviously wet. It is at this point that you will want to stop adding more water. And, if you succeeded, the dough will be tacky. I will usually remove the dough from the bowl at this point and knead the dough by hand for about 30 seconds to a minute. This improves the hydration a bit more and slightly diminishes the tackiness and allows you to shape the dough into a tight, round ball. If you'd like, you can check the dough at this point to see if it passes the window-pane test. I no longer do this myself but you might want to try it just to satisfy yourself that the dough is in proper form. The dough can then be placed within a container (after lightly coating the dough ball with oil) to go into the refrigerator, either immediately after coming out of the mixer bowl (my preference) or after an additional room-temperature rest period as called for by the Reinhart recipe. BTW, there is no need to use a storage bag. If you'd like, you can use a covered container with a cover that will better contain the dough as it ferments and spreads out. I use a metal cookie tin with a snap-on lid.
I think if you try the above approach you should get better results. It is the basic approach I use for almost all my doughs made in a KitchenAid stand mixer. You will most likely end up with a dough that stretches too easily but that will not be because of the approach you used to make the dough but rather the recipe itself. But the pizza should turn out fine, especially in an oven such as yours.