I have read on many occasions including on the Fibra Ment web site that thicker stones require less recovery time due to the fact that the mass of the stone holds more heat and looses less during baking.
Yes, but... That's great marketing, and in a strict sense it's "true", but I doubt it matters all that much at home. Besides, other considerations may be equally or more important: thin pizza stones crack more easily; and desired thickness depends a great deal on whether you leave the stone in the oven or pull it out and serve the pizza still on it, as if you pull it out of the oven you want to keep the weight down.
I have done a search here and on Goggle but to this point have not found any specific timed recovery tests. I bet they are out there, perhaps one of our more knowledgeable members has that data.
I have been watching and looking for several years in the context of breadmaking, and have never ever seen the results of a timed recovery test, so it doesn't surprise me that you haven't found any either. Besides, so many things other than the stone itself matter, things like: the kind and shape of heating element, the amount of insulation in the oven, which height the rack is set at, and the type of thermostatic control in the oven.
If I read http://www.californiapizzastones.com/
correctly, they provide the 3/4 inch thickness for home use and classify the 1 inch thickness as "industrial". My experience in the context of breadmaking is that "industrial" accessories are not a good idea, because they expect to be used in an "Industrial" oven and don't work very well (sometimes they don't work at all) in a home oven.