Good idea. I would take out the plastic foundation frames and move the capped honey/pollen to the outer edges. Then put the empty frames one frame in from the outside. The intention is to make the bees cross the empty frames to get to the honey. That way, they will consider them part of the brood nest and probably work them sooner. I would probably leave the feeder in place until it is empty, then take it out - don't refill it.
Is the plastic foundation waxed? If not, it is going to be a real struggle to get the bees to use it. If it is, the same trick might work to get them to use the frames, but I would try the foundation less ones first.
That might work if they are waxed. Probably won't if you leave them at the outer edges of the hive though - they seem to have decided that they are "walls" for now.
Any box (Flow super, brood box, traditional super) should only be added when ALL of the below are true:
1. All frames have fully drawn comb across most of the frame, and
2. The comb is 80% full of honey, nectar or brood, and
3. Every frame is well-covered with bees
That way, you know that you have enough bees and enough motivation to use and defend the new space.
If you do that, you are putting the honey harvest before the well-being of the bees. In your region, I think most people use 2 brood boxes for overwintering. If you put the Flow super on, they won't have time to fill a second brood box as well before winter. It is your choice, but I would go for the second brood box first, and accept that I may not get a honey harvest this year. Next year you will have a much stronger colony, and you will be ready for the nectar flow much earlier.
If you have a nectar flow, one feeding should be enough. If there is a dearth, and they need to draw a lot of comb, I would start feeding again.
Good luck to you and your bees! I look forward to reading @Martydallas's advice.