Extension of Bressoud's generalization of Borwein's conjecture and some exact results

In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Finally, using certain positivity-preserving transformations for $q$-binomial coefficients, we prove the non-negativity of the infinite families.
Comment: 17 pages, 2 figures. Dedicated to George E. Andrews and Bruce C. Berndt in celebration of their 85th birthdays. Comments are welcome!