I'm still working on this. Right now the most attractive options for me are (i use 1 2 ... 9 A B C for the twelve elements):
Option 1: (this is what we have been looking at before)
1 2 3 4 5 6
4 5 6 7 8 9
7 8 9 A B C
A B C 1 2 3
Option 2: (same as option 1 but add two more pillars for extra versatility)
1 2 3 4 5 6
4 5 6 7 8 9
7 8 9 A B C
A B C 1 2 3
1 3 5 7 9 B
2 4 6 8 A C
Option 3: (similar to option 1's "cyclical overlap" style but with 6 pillars instead of 4)
1 2 3 4 5 6
3 4 5 6 7 8
5 6 7 8 9 A
7 8 9 A B C
9 A B C 1 2
B C 1 2 3 4
Option 4: (again cyclical overlap but with 12 pillars)
1 2 3 4 5 6
2 3 4 5 6 7
...
B C 1 2 3 4
C 1 2 3 4 5
I'm still investigating other options but these are the front-runners for me right now. I plan to do a more general analysis before i commit to any one recommendation, but this may take some time so i thought i'd just give a quick update. All comments are invited (as always).