I have rewritten my draft article Products in dagger categories with complete ordered Mor-sets. Now I denote the product of an indexed family $latex X$ of objects as $latex \prod^{(Q)} X$ (instead of old confusing $latex Z’$ and $latex Z”$ notation) and the infimum product and supremum coproduct correspondingly as $latex \prod^{(L)} X$ and $latex \coprod^{(L)} X$ (“L” stands for “lattice”).
I am going yet to rewrite this article to allow partial products to be defined and used, as it is required in my further research.