My understanding is that these isolated runestones deep in North America, thousands of kilometers away from any other evidence of Norse presence, have about zero value as archaeological evidence. It's hard to come up with a story for how a genuine ancient Norse artifact could get there like that that is even remotely plausible. Modern hiking ethics are a pretty modern invention. Usually, when people go on expeditions like that, they leave a trail of trash behind them. And nobody's going to make a clean hike thousands of kilometers into an unknown land without leaving any traces, then stick around somewhere long enough to carve "gnome valley" in huge letters on a rock - which must have been roughly the plan all along, too, because otherwise, why did you pack stone chisels for the trip, and if you didn't pack them, then where's the on-site smithy? - and then just fade into the mist, again leaving no trace.
Carved rocks are somewhat too convenient of fodder for mysteries like this, because they're just so difficult to date. I think that the most plausible hypothesis for the Heavener inscription, though, is that it really is of Scandinavian origin. But that it dates to the 19th century, not the 11th. This is based on three things: The only thing about it that looks remotely medieval is the simple fact that it's using a runic alphabet (the vikings liked to decorate their runestones), and it is reportedly somewhat nonsensical in Old Norse but reasonably straightforward to read in a modern dialect, and we know from the historical record that there were Swedes (IIRC) living there around then.
I understand the doubt about the Norse origins of the Heavener runestones and others found in the area.
Automatically assigning them to a 19th century origin date based only on the presence of Scandinavian immigrants in the local area totally ignores the historical evidence that the author of that site dug up and laid out in that horrible format.
I suggest that you read through the entire page to the end. It will be a slog but it offers a much more believable origin story than that of Scandinavian immigrants carving a few stones and scattering them at widely spaced locations on the landscape.
The French had a much friendlier relationship with Native American tribes and had explored a lot more of North America before the first settler ventured west from the colonies to see what lay past the Cumberland Gap. I am obviously more inclined to believe the author's (taking him at his word) well-researched account of events leading up to the inscribing of the stones in Oklahoma since they fit closely to historical documents and accounts taken from eyewitness records.
The whole story of La Salle's attempt to reach French settlements so that he can save those left behind in Texas is well known from contemporary Spanish and French records. The accepted story that La Salle was murdered by his own men in Texas probably needs to be discarded since, as this author documents, the route they took, the terrain they encountered, the distance they travelled and the azimuth do not agree with an end point for the murder occurring anywhere in Texas. It does however closely agree with that murder having occurred in Oklahoma or far west Arkansas.
Carved rocks are somewhat too convenient of fodder for mysteries like this, because they're just so difficult to date. I think that the most plausible hypothesis for the Heavener inscription, though, is that it really is of Scandinavian origin. But that it dates to the 19th century, not the 11th. This is based on three things: The only thing about it that looks remotely medieval is the simple fact that it's using a runic alphabet (the vikings liked to decorate their runestones), and it is reportedly somewhat nonsensical in Old Norse but reasonably straightforward to read in a modern dialect, and we know from the historical record that there were Swedes (IIRC) living there around then.