I'm seriously a newbee here, but I would say you need to giver her majesty some room to lay. You could move some of the drawn/filled comb up and insert some foundation in between the comb remaining. In the brood chamber my understanding is that they will draw out frames of foundation between already drawn out frames. Putting foundation between drawn *honey* combs will cause some problems, though.
This spring (being a newbee going into the spring with my first hives) I had a regular swarm rodeo going on. I had fed one hive I believe for too long of a time, but the other two packed themselves right out room. I looked in there and all I could see was glistening honey/nectar like you've mentioned. :( My problem was that these two hives were in a deep and I was trying to go all medium 8-frames...I didn't figure out how to move up the drawn frames and wasn't sure of putting mediums in the deep. In hindsight, I should've just did it to keep the bees at home and worked it out later.
Could the colony be trying to pack the queen out of laying to get her ready to swarm? I know your flow is on but has your swarm season already passed?