Ok, small update/discovery. Still not sure what the other 12 cards are - however, I think I have a release year.
I remembered these identification pamphlets that I also picked up from the Ohio Division of Wildlife. (Again, probably at a nature center or something like that). There were all kinds of different ones, but most importanly for this post, there was a "Sport Fish" one. Well, I dug mine out and flipped it open. Right inside the cover was that same Sport Fish Restoration logo that Lea DeFoote pointed out. Then I flipped to the fish, and what do you know, the artwork is exactly the same! I'll link the Bluegill in the booklet versus the card here:
Booklet page
Card
Unfortuantly, there seems to be no correlation between the order in the booklet and the cards. Not only that, but there's 30 sport fish listed, so I guess some didn't make the cut for the card set. All the cards I have are also in the pamphlet/booklet, though.
On the back, the booklet has the publication date listed as 5/23/2008. So, I think it's a good guess that 2008 is the publication date for the cards as well. I can't imagine finding anything better for a release date for the cards than a pamphlet, put out by the same people, that uses the same art, which has a print date on it.
Back of booklet (date in text at bottom)
So with the year, the knowledge that the set (should) be 24 cards, and the ability to scan in half of them, I plan to submit the checklist in the near future. I'll name the 12 unknown cards in the set TBD so they can be added more easily if/when any more ever pop up. Assuming there is no objection, obviously. Please post below or message me if I shouldn't add the checklist as planned.
And in the meantime, if anyone finds any card from #13-24, please let me know so I can add it to the initial checklist. Thanks!