Would a pva glue with a ph of 4 be suitable to mount primed linen to hardboard?
That is rather acidic and would likely cause some degree of acid hydrolysis. There are PVA sizes that are buffered to be neutral. Two of them are Lineco pH Neutral adhesive and Gamblin’s PVA size. Acrylic dispersion gel mediums are also good choices. We discuss the subect more fully in ourAdhesives and Sizes downloadable PDF found on this page https://www.artcons.udel.edu/mitra/resources
I really like Acrylic Gloss Gel Medium for this application. I coat the fabric and panel separately in advance and allow both to dry before mounting with an adhesive coat of gel. (Fabric is stretched for sizing.) This way, I can mate two acrylic-coated surfaces for an excellent bond with very little shrinkage of the fabric. On the rare occasion any blisters or unbonded corners develop, a warm iron tacks down the loose bits once the adhesive is dry.