Here is a pic of what I meant.
This is just to show all the different lengths for a 3x3x3. You wouldn't put that many bars on at one time!
With bars of different heights, you have another level of bandaging. Sometimes the bars can pass under each other, sometimes not. Another 'bar' that would add interest would be a simple vertical rod, this would not pass under bars but wouldn't bandage any pieces together.
An interesting puzzle?