Thanks to Matt from Heartbreaking Cards for identifying this set for me. It is the 1971 Dell Today's 1971 Team Stamps.
I discovered there were 25 albums in the complete set, each with 2 pages of 12 player stamps each. The set that I have comes from their All-Star album. The stamps were perforated for easy separation, but once separated there were no spaces in the album to put the stamps. The cards were unnumbered. I still have no idea why these stamps were laminated and if they were sold that way. Another mystery remains to be solved. Thanks again Matt!