As there is no rewards, there are no strategies apart from trying to double spend, and the odds that you can do it because you happen to be the preferred staker on the false chain are small.
What about censorship?
I don't see the problem. Why would an arbitrary minter censor you ? And if he censors you, the next one probably won't.
The problem I see with minimal or no minter rewards is that minters wouldn't lose much by not mining (or only mining on top of selected blocks), which lowers the amount needed to bribe them to perform any action desired by an attacker.
Who are you going to bribe ? The guy that just minted a block, but if he changes something, he's not the preferred minter any more, but some other dude ?
The idea is that, if the preferred minter order is a random function, depending on every individual bit in the block, you cannot know who will mint the modified block !
As iamnotback said, this is just at high conceptual level and not a "design", but essentially, you take a hash function of the block, and you find the Hamming distance between this hash result and the minter's stake address. The one with smallest Hamming distance is the preferred minter. Change one byte in the block, and the preferred minter becomes someone else. Many minters can mint blocks almost simultaneously. Another function will tell future minters which chain to prefer to mint upon. This function should be well-designed so that there is almost no way to "orphan" many blocks, by increasing exponentially the preference for the currently longest chain.
I'm not doing anything PROPORTIONAL to stake - you simply have to stake a given amount, somewhat like the master node scheme in DASH - but the amount shouldn't be very high - as there's nothing to WIN in staking, you don't care about your probability to mint, you only do it altruistically to keep the network running.