Buttons,
Welcome to the forum. The solid back is fine, you will still have plenty of airflow.
I have built dozens of cages, and have found wood and water are not the best combination, even if you seal the wood, water tends to travel, and mold will often be the result. I have moved to plastic shelves from hardware stores to be my bases, and buy screen 24x24x48 cages. You can get all the screen pieces at hardware stores and build your own custom cage.....
I am not sure what you mean by 1/4 round, 1/4 round to me is moulding around a floor, you may want to clarify that term for others.
That being said, if you want to build a custom enclosure, think about water management first;are you going to use automatic misters or drip containers, how much water are you flowing through the cage daily, how will you collect it so it does not end up on your floor, and what container will the waste water end up in.
One other thought is to have one cage for the balcony that rolls or is easily carried, that can serve as both the big indoor cage and the balcony cage.
Enjoy the process of making your habitats for your new dinosaur!
Nick