This really is a nice interesting challenge. At first I thought you were forgetting part of the game mechanic or something but boy was i wrong. After a couple hours of tinkering I got up to 9597, so those claims are obviously correct. the 11k I really do think is impossible, unless some radical new design I can\'t see is responsible.
The easiest way i know to describe it is. X=block, O=space, and stack the layers on top of eachother. The pattern is pretty easy to get, and you can see how it could be applied to larger spaces. (note layer 4 is different from 2)
X O X X X
X X O X O
X O X O X
O X O X X
X X X O X
O X O X O
X O X O X
O X O X O
X O X O X
O X O X O
X X X O X
O X O X X
X O X O X
X X O X O
X O X X X
O X O X O
X O X O X
O X X X O
X O X O X
O X O X O
X O X X X
X X O X O
X O X O X
O X O X X
X X X O X
It should be noted that while it is space efficient, it is not mass/blocks efficient. The same 78 blocks I used can be arranged in a conventional large 3d cross for 31,358 power/sec, so if your end goal was to use this on a cloaker there are more efficient setups.
on a side note this problem can be brute forced, by running every combination of each space either having a power generator or not. However that\'s 2^125=4.25*10^37 which as far as i know is FAR out of the range of the world\'s most powerful computers to do in a reasonable time.