Now I read that the Chinese peonies (Lactiflora) holds its leaves right to autumn. That variety sounds like it would do better here, but doing this will limit my choices considerably.

I notice that Hollingsworth Peonies will openly state if a particular Hybrid is susceptible to die back in the heat of summer. From your experiences, do you think I need to limit my peonies to the Lactiflora types only?

I'd suggest a couple of local field trips to see how the different varieties look in this region throughout the summer. Andre Viette's in Fishersville (about a half hour away from you) has fields and fields of the herbaceous hybrids, and Lewis Ginter Botanical gardens in Richmond has an extensive collection of all types scattered throughout the Asian Valley and perennial garden. You can't really get or plant any bare-root peonies (which is mostly how they're shipped) until fall anyway, so you may as well do some observational visiting this summer. Have fun!