Even though you haven't convinced me with the plan as briefly described, sure
. I will assume that the pizza you make will be edible enough that you dare serve it to your wife. If so and she uses the term "Daddy" as a result, I will concede defeat.
However, to round out the picture, I went back and searched my early posts where I described doughs that I made using small amounts of natural starter with long fermentations at other than in the refrigerator. As best I can tell from that search, the longest fermentation period I achieved, using my wine unit at about 55-65 degrees F, was a total of 44 hours. I described my results at Reply 94 at http://www.pizzamaking.com/forum/index.php/topic,986.msg25807.html#msg25807
I didn't mention it earlier, but even if one can achieve very long room-temperature fermentations, the longer the fermentation period the greater the likelihood of significant damage to the gluten structure due to attack by protease enzymes. I alluded to some of those problems in the post referenced above. One might be able to slow down the enzymes by using more salt, but the amount of salt to do this effectively might be more than one would be able to tolerate on the palate.
Another possibility is to use a poolish or like preferment with very small amounts of commercial yeast. However, the prefermentation time wouldn't be tallied as part of the total 3-4 days window.