I spent a long time trying to find a unique design with the Kura bed frame but just wasn't satisfied. Finally I realized that none of the designs I found attempted to turn the bottom mattress perpendicular. This was a game changer for making the Kura to a twin and full bunk bed.
As you can see in the photo, the top bunk is a normal twin. But on the bottom I built a simple platform with 1/4 plywood and a footprint slightly smaller than the full size mattress I wanted to use. I used some basic lumber from the store to raise the platform to the height of the Kura frame which which runs along the base, since that was the real "gotcha" with this approach. Basic lumber sizes were not a perfect size match, but that is not noticeable when sleeping. I put the supports on all edges and spanning cross in a few spots for support (I wanted to ensure it would support me). I left a gap for the Kura frame cross bar on the floor, which almost snapped into place.
As an added bonus, the Kallax 2x2 fit under the bunk next this mattress almost perfectly for books, light and a clock!