So the mystery miner seems quiet at the moment, nonetheless...
One of the elegant bits of bitcoin is that you can't start hashing a new block until you know the inputs, that is the new transactions you're going to have to hash, amongst other things.
If you decide to mine empty blocks, you take away one of the 'freshness' inputs that mean you can't work on the hash 'before time'. You are left with the hash of the previous block, and the time of your new block (am I right this is an input to your hash too ?) as things you're going to have to guess to get going early.
Normally the previous hash would be a large number, up to 256 bits, infeasible to exhaustively search while also searching for low hashes. However the bitcoin protocol also means that you know something about the previous hash, it meets the difficulty requirement, so your search space is reduced.
With a combination of choosing a time sufficiently far in the future and hashing with low input hashes only (changing the hash rather than the seed for instance), is there an advantage to be gained over other miners by trying to compute before the previous block is published ? Is this advantage increased if you wait until you have two valid hashes in a row before deciding to publish one ( if that's it, this should be easy to spot in the delay between mystery miner after someone else vs after himself) ? If there is an advantage does it increase as difficulty gets harder, making empty blocks trivial to find when difficulty is near the end ? You also have to gamble with the times, did the mystery miner blocks have odd time stamps ?
I'm sure you can set me straight, I have a nagging feeling that one exhaustive search is as hard as another in this case, at least until a long time in the future, so I should just accept that there's a lot of new hashing power, but if there's anything in this I would support moves to restrict empty blocks - this would comprehensively prevent such an attack