The Ballstreet Cubs sheets mystery has been solved!
A different reader named Chad left a comment that my sheet came from the August edition of Cubs Quarterly Magazine. I went to Ebay immediately and searched Cubs Quarterly 1992.
Here's the cover of the August edition. The cards are even mentioned on the cover.
There they are inside the magazine.
I looked over the other listings and found the other sheet, the one that Kevin showed me.
It is in the June-July edition.
I've already bought a copy of the June - July edition, but not the one above that shows the cards. The one I bought was just $5, compared to the starting bid of $20 for the one above. Hopefully the one I bought still has the cards inside. Stay tuned.