If we took your interpretation and comments here about carrying a firearm openly in our own homes, then that would me I couldn't clean, handle, repair, or otherwise do anything with a firearm "openly" within my own home. Do you think this argument makes any sense whatsoever?
Only if it makes sense to clean or repair a loaded firearm.
So, what I'd like you to do instead of trying to over analyze the law, I'd like you to find me a court case here in Oklahoma where the laws you mention were applied, and someone was punished for "illegal carry" within their own home. That's really all that is going to matter. There is a very, very old case where courts upheld the fact that it was indeed illegal to carry outside your home openly, and on your own property. However, the law appears to not have been challenged again with the addition of the self-defense act, and the current climate of being more open to carrying firearms. I believe the courts would rule differently now.
Here you go. Gilio v. State, 2001 OK CIV APP 122, 33 P.3d 937. Refused to address the question of equal protection, but is worth a read.