Is your aim to add a) high level of ventilation year-round, b) monitor mite fall, or c) reduce mite populations in the hive?
These are somewhat different goals, with somewhat different critical paremeters, I think.
I run both screen and solid boards, together and year-round. Mine are optimized for my primary goal which is having a way to do mite counts, very frequently, and year-round. Note that I am north of Albany, NY, so yes, that means I do them in the winter, too. (Just for my own curiosity since there are no published thresholds for treatment during the winter.)
For simple ventilation, wire (not plastic) window screening would work, I think. I must say, however, that even though I read that some people do use SBB in the frigid North in the winter, it chills my bones just to think of it. I keep quilt boxes on top to provide for excellent moisture management so even with a solid BB, I wrap shipping foam sheets around the closure of the monitor slot to seal it up from the cold drafts. But if you're OK with that (keeping a hive at CT ambient winter temps), then window screen would work. It will get gummed up with all the hive debris pretty quickly, and scraping that stuff off will just mash it into the tiny pores, plugging it up like kitchen sieve, I think.
For varroa monitoring purposes you will need to have the floor material be similar to #8 to allow the wretched beasts to fall on through. Otherwise I think it would be impossible to assumme the treatment thresholds are valid because some would escape being counted. And the slot that allows the tray or board to be inserted must be closed off from access by other bees to preserve the mite sample.
For varroa suppression purposes (something that I see mentioned occasionally, but that I don't think works well, at least based on what I saw during my nearly-constant counts last summer), you'd defintely need something that allowed the mites to fall out of the hive en masse and a way for the bees to be prevented from casually re-encountering them outside the hive which might allow them to hitchhike their way back inside for a second chance.
The other issue I have with plain (no solid BB below) screened BB is that last summer during robbing season I observed some bee-felons occasionally sneaked in past a mis-inserted wooden closure thingy and tried to get into the hive from under the screened floor. This really upset the bees inside and seemed to me to be a decent chance for additional mites to be brought in by the robbers to transfer directly into my hives.
As for SHB, I can't see why you'd want any of their larvae to fall out on to the soil so they could pupate. I don't have a big issue with them, but when there is a small increase I found that a twice-a-day pulling of the boards captures enough larvae clinging to it (and which I then squash) that it quickly brings things back into control.
Maybe there's something bad that I'm not seeing about running both boards at the same time, but if you already have both of them why abandon a good solution and carve up your solid boards?