There's no consensus beyond "obvious fakes."

I was unable to find much on these outside of the same images and text repeated across the various websites and books. Looks like I'm not alone in that. Colavito usually does a great job on his write-ups, so I'm assuming if he didn't find anything, it's not out there. The Arizona State Museum has since updated their website with information on the slabs, which is still fairly limited. In short, we don't actually have any idea where they came from and they look nothing like any thing else found in the Southwest- or the world. I'd like to reemphasize the fact that

What can we learn from the way people have talked about these tablets?

For one, it's interesting to see the diversity of explanations. A frequent one is that they are authentically Native American and depict mammoths that survived the supposed extinction dates. This is the interpretation supported by your link, and it's also one that appears in a handful of Young Earth Creationist sources. This theory is generally crap; the claim that there are images of elephants in Copan and Palenque, for instance, is based on the artist I discuss here, who literally just made things up. Others believe they are the result of interaction with Mali. This Mormon author, whose works are typically called "proselytizing," believes it's evidence for ancient contact with the Levant that supports the Book of Mormon. Still others suggest Asia or Ireland as the origin. This should be an instant red flag. Objects with so little consensus are hardly ever authentic.

Another red flag is the paucity of sources. Nearly everything I could find relies on the same text found in the 1971 Science Digest article quoted in your link. This is, of course, a magazine known for discussing UFOs. The quote from Earl Halstead Morris appears to originate in that article, as I can't find it anywhere else. This single source is regurgitated by people with singular agendas: validate the Book of Mormon, promote Evangelical creationism, prove ancient African connections. The linked authors aren't experts in any one thing, rather they pick and grab whatever evidence they can find make it fit the unifying theme of everything they've written. When nobody else is saying that the slabs represent a connection with Africa, for instance, but an author like Clyde Winters, who puts out a new book every other year which erases indigenous American history in favor of his pet theories about African empires on the continent, you really have to wonder if they are actually looking at any evidence for that claim. When everything an other writes has to do with, say, proving the existence of elephants in the Americas, it doesn't mean much when they claim a suspicious artifact is evidence for elephants in the Americas. When all you have is a hammer, everything looks like a nail.