Thanks to those who were kind enough to respond to my question earlier about sweet barbecue sauces. I have found a product that is exactly right for me.
http://www.lloydsbbq.com/products_wf_pulledPork.asp
My one issue was avoiding sweetness in the sandwich, didn't care if I bought the sandwich at a barbecue place or assembled it at home. The above Lloyd's non-sauce-covered "Woodfire" Barbecue Pulled Pork is made with very little sugar evidently, as I didn't discern any in the taste. I have difficulty with finding a non-sweet barbecue product in stores, including Lloyd's barbecue products as well, those few which I have tried seeming to be aimed for buyers who do like sweeter sauces--or at least my own experience has been that, though I haven't tried all products.
The only product i have found is this Lloyd's Barbecue Pulled Pork, which is outstanding in that it does not IMO have a sweet taste! (IMO, of course, can't guarantee that others will have the same thoughts.)
They also make a shredded brisket "Woodfire" as well. I haven't tried it and won't be in any hurry to--though I probably will eventually--because the label indicates brown sugar and molasses in the ingredients, as well as regular sugar. OTOH, the pulled pork is pork, cider vinegar, sugar, sugar, salt, spices (and the sugar I couldn't taste!--or did I already say that?

) Also a shredded chicken Woodfire, which also has a long list of ingredients.
I'll stay with the shredded pork "Woodfire" for now.
If your grocery store carries either, it will probably be either in the deli or meat departments, but in any case wherever the "blister-packaging" meat products are sold.
Perfect sandwich, toasted whole wheat bun, fairly lean--just right--pork with slight vinegar taste maybe, not sure--topped with coleslaw made with olive oil and vinegar, with mustard on the bun. ^
NOTE: It MUST say "Woodfire" and "pulled pork" on the package! Otherwise, wrong Lloyd's product!