Well, the bees don't determine where to lay according to the size of the box. The only barrier to the queen is the space between the brood box and super. It works, and old time hives were designed with that in mind. I always wondered what keeps a 2 brood box hive running.
So, "putting on a super" is really just setting it up for beekeeper honey robbing. The bees don't see it as tribute, they will use it for stores as well. I'm just using one deep and a shallow, because I'm out of usable hive bodies. They've filled the brood chamber(s), and I'm worrying they aren't filling the supers. About July they stopped drawing comb; period.
From what I'm reading here, it seems they stopped brood production at the start of the dearth, went through their stores waiting for a break, and have started to build stores again. With the stores, you should see them building brood. Since that's what we're worried about, I would think the plan of action here would be to feed them 1:1 syrup. Since you have the frames drawn, I would keep an eye on the stores and avoid having them go honeybound. Remember, they need protein as well.
I have a chair set right next to the hives, whenever I get a break I sit and watch what they're doing; my nose about 12 inches from the entrance. Right now no pollen goes in after 10 in the morning. But the pollen is going in. They don't mind some sub, but I don't want to feed the beetles. Sometimes they surprise me in the late afternoon with a cloud of bees hovering in front of the hive. I know it's orientation. What are your bees doing?