The redundancy rule says
"large ships can ignore the effects of a certain number of critical hits every turn. They still take the extra damage as normal, but the aditional 'effects' on the critical table are ignored."
The redundancy rule only cancels the effect, so you still have to role on the table to see what the crits are, and what damage they cause. The way we play it is that it cancels the first crits rolled each turn, you don't get a choice.
Going by the example you gave (1,1,4,5,6,) would see the 4,5,6 results get through as normal, with the two 1 results absorbed by redundancy. But say that the five crits had come up 1,6,4,1,5. The way we play it would see the first 1, and the 4 effects (not the damage) cancelled. The second result, the 6, being a vital system crit would get through. Uneffected by redundancy.
We just liked the way that this seemed to represent catastrophic damage, that was beyond the ability of redundancy systems to cope with.