You have gotten so much good advice. Feed!!!! You need them to draw out comb. Feed them 1 to 1 sugar water. If the flow is not on, they will take that sugar water and use it to build comb. If the flow is on, they will probably ignore the feed and go for the natural stuff, using it to draw comb. Give them feed "just in case." I bet you could find a local beek who would be happy to come over and assist as you get your hive settled and re-homed.
One thought about foundationless frames...You need to be very deliberate in the way you handle those frames. You will have a foundation hive next door, and you will be tempted to be "lazy" about the way you handle frames in that hive. You can flip foundation frames every which way to look at what you've got. Not so in a foundationless frame, especially when it is hot out, it is newer comb, or they haven't attached at least three sides. I have run and do run quite a few of both. I suggest that you form a habit of treating every frame as if it were foundationless. Don't get in the habit of holding combs angled parallel to the ground. Keep them perpendicular to the ground and rotate on the long axis. (You can search for demos of people handling top bar hive combs, to see the best way to rotate foundationless frames of newer comb) Why do I make this suggestion? Because on a hot day this summer you are going to not think about it and flip a foundationless frame sideways and drop the comb on the ground. So, treat every frame like it is foundationless, in order to ingrain that habit in your brain.
Have fun with it.