Barley Wines are the strongest of beers checking in at almost wine strength alcohol. In obtaining that strength of alcohol in a beer an excess of unfermented sugars are often present. Thus, barley wines are sweet on the palate and additional bittering hops must be added to prevent the beer from being cloying. Very high alcohol strength beers (up to 13%) can be brewed with belgian yeasts that are not overly sweet but the flavor profile is different than a "regular" beer. Barley Wine is basically an English style of beer using English style yeasts (great variation here but its a good guideline) which do not have a the alcohol tolerance of Belgian yeasts (which are often mutated wine yeasts).
These are beers to be sipped and a full 12 ounce bottle is an awful lot, unless you want to consider it a "split" between two people. They are best aged, like a wine. For optimal drinking, depending on the beer, year brewed, aging conditions, etc. I would recommend 2 to 5 years. for cooking, aged is probably better as the bitter hops will die back and not bitter the dough, unless that is what you want. I'm sure such a beer would express its flavors in a pizza, you seem to be moving toward very full flavored and high alcohol beers in your quest for pizza dough. Unless the beer is in a Belgian style, higher alcohol will point toward greater residual sugars and more intense flavor.
Is ok not to like a beer. Not every beer is for everybody, but, for me, every beer is ok for this somebody. If you like this barley wine, try Bigfoot from Sierra Nevada, its the ultimate American style Barley Wine, at least for me. I recommend 3 years of age although it can go longer, I currently have bottles back to 2004 and they are great, not the "sweet spot" but really good.
If you can track down a bottle of Hunnapuh, from Cigar City in Tampa Florida, I think it would have an immense impact on your dough. If you can't get Hunnapuh (its really difficult), then try to find Marshal Zhukhov's from Cigar City, about 13% and intensely flavored Imperial Stout (a Barley Wine style Stout).
Good Luck, I love commenting on this thread, personally, I like my dough plain but your escapades are fascinating to me on a beer level.