We have a collection of similar stones found in southern Texas and northern Mexico but none as big as the one pictured.
Your “stone hot dog” might have been used for rolling something out flat. I found a stone needle or something used for punching a hole in leather, possibly.
I have another interesting stone, it’s small, with a hole in the center top and grooves where line or something must have been wrapped around it, possibly a sinker for fishing, since it was found on the beach. We also have a collection of round rocks that resemble soft balls. I am told that they were known as fire rocks and were used for ceremonial purposes around the edge of fires. I was also told that I was not permitted to pick them up and take them. Too late.