Holy cow, Frank....nice to know I was not the only Bottle Cap Weirdo in the neighborhood. Actually, it was mostly my neighborhood boys who did this, so I was one of the "Girl Exception To the Rule."
I also collected the earlier ones you mentioned, with the cork linings. So, those ones you would not have normally had, just because I was much older than you - and those special caps faded out of existence. (Grape and Orange Nehi, among others)
Those vacation resorts that also had a small grocery store? They usually had a large soft drink cooler on their porch. You opened the lid, dug in, chose your drink of choice, pried off the cap - in a convenient "cap prier thing," in which said cap then fell into a lower repository of the cooler. Then you went inside and paid for your libation.
Sometimes, I would be able to use my "adorable little blonde-curly haired small girl charm" - learned from Shirley Temple movies - to coerce the store owner into giving me all the discarded bottle caps in the cooler's repository.
It worked, and that is why I always came home with a new treasure trove!!