A question about low-tech humidity control

My first oyster pins appeared today and I've been thinking about humidity control. I have this big tub I made my still air box from and I've been wondering about using it to hold the two fruiting bags I have. I was concerned that maybe the X slices wouldn't get enough fresh air if I covered them, but then I've been worried about keeping up the humidity. Now that I'm seeing some pinning though I'm feeling like the humidity is more important? I live in Colorado, which isn't quite desert but the humidity in the house typically drops below 40% during the day (it's high right now because we've been getting some rain showers).

For reference, my SAB is a typical DIY, made from a large tub with just a couple hand-sized holes cut out. There's not a lot of airflow in that room anyway, and I'm not sure how much fresh air the mushrooms need once they start growing. Of course I realize they won't be able to stay in the SAB too long, I know they'll outgrow the available space, but I'm just thinking for the next few days, or however long it takes them to really fill in.

So, any thought on this? Should I close them up in the box or just leave them in open air?