Welcome!!! I am a native Texan. Born there anyway.
regarding the piece in question, to me it looks like *the groove* is a completely different material. Like the stone had a vein of another material running through it. Is that the case, or has the polish completely change the appearance of the rock?
Your rock is formed by natural erosion and is caused by one part of the stone being comprised of a softer stone which would erode at a faster pace than the rest of the stone. If it had been an actual Hammerstone or Maul you would see evidence of battering on the ends and I don't see that in your pictures.
I find these quite often and I call them "Cookie Rocks".
By the looks of your collection on the shelves you have been busy to say the least. Thats some nice looking worked stone. The first rocks you posted are natural but everything else I saw looked quite good. Welcome to the site, rock