It is quite likely that we may never find out who private brands the Great Value whole-milk mozzarella cheese for WalMart because of the confidential and proprietary nature of such arrangements. Most likely there is more than one source since WalMart almost never sole sources any food product.
You are correct that the Kraft website identifies several WalMarts in Texas as potential sources of Polly-O mozzarella cheeses. When I checked the Kraft website, I saw about 10 Polly-O mozzarella-based products (no cryopak versions), of which two were indicated as being sold at several WalMart locations within a 20 mile radius of my zip code. The website also had a statement near each product that read as follows: "To ensure this product is currently available, please contact the retailer". When I couldn't get an answer from anyone on the telephone, I went to the two WalMarts closest to me and spoke in person with a total of four people in the cheese departments. While I was there, I saw about seven or eight brands of mozzarella cheese, mostly national brands, but no Polly-O cheese. To make matters worse, none of the four persons I spoke with had ever heard of Polly-O, and none was aware of who private brands the Great Value brand of whole-milk mozzarella cheese for WalMart. When I mentioned that the Kraft website lists WalMart as a possible source of Polly-O products, I was told that that didn't mean much since WalMart was not obligated to carry every product for which it is an approved seller or to carry any such product at all times.
As I previously reported, Polly-O is a small company that serves mainly the eastern seaboard. When I spoke with a Kraft customer service rep some time ago, all the states she mentioned were east of Georgia, with the bulk on the seaboard from Maine to Florida. The Polly-O website also says that they mainly serve the eastern part of the country. The customer service rep, a long-time Kraft employee, had also personally indicated doubt about Polly-O's ability to private brand mozzarella cheeses to WalMart (because of Polly-O's small size and limited manufacturing capacity). A quick Google search shows that there are over fifty domestic producers of mozzarella cheese, many of whom have national distribution and are already selling cheeses to WalMart and could also be doing private branding to WalMart. All things considered, I see little or no evidence of Polly-O being the private brand source of the Great Value mozzarella cheese.
I have not been able to find any Polly-O cheeses locally so I have been unable to do any side-by-side comparisons with the Great Value whole-milk mozzarella cheese. However, Randy is familiar with both the Polly-O cheeses and the Great Value cheese. I don't know which precise cheeses he has compared, but I am of the impression that the cheeses he has compared were different. When I am back east next time, I plan to locate the Polly-O whole-milk mozzarella cheese to be able to do my own side-by-side comparisons.