The attacker doesn't even need a 51% stake. They only need a small stake, once you can forge once, you can ensure that you will always gets to forge the next block (if you have enough computational power), regardless of how small your stake is. I can easily see this attack being possible with 0.1% stake and a standard processor.
I agree with the fact that it can be attacked with less than 51% stake. How little stake can be used depends on a couple of factors. The time since last signing and balance are weighted in the "difficulty" of finding a hash so I am not comfortable putting an exact value on how little stake can be used. That would require some simulations.
In general though one could say that the structure allows a forger (any forger) to use computing power as a proxy for stake. The effective share of the network is dependent on not just what share of the stake one has but also what share of the computing power.
While NXT claims to not be PoW if forgers aren't already using computing power to boost their returns they will. Even non malicious miners would have no incentive to not increase their computing power in order to boost their forging rate.
As a side note: deterministic (or quasi deterministic) signing/minting/forging is an interesting idea. ... The full implications both good and bad should be looked at more closely.
The problem is that you are still vulnerable to historic attacks. ...
That is a good point. I agree and it requires some careful analysis. I do think it an interesting idea and has some potential. On your idea of cummulative work it may be possible to incorporate a way to compensate those worker. I also believe despite my reservations about PoS that there is some way it can be used in conjunction with PoW to raise the cost of an attacker. PoW for Bitcoin is already beyond the point where any economic attack is possible however there is the non-economic attack. The network will continue to grow and as miners become more efficient ($/GH and J/GH) the cost for an attacker will rise but eventually margins will be paper thin and further improvements will be limited to the growth of the reward (Moore's law doesn't make the network more secure as it is kinda like GH inflation). I believe PoS could be used to raise the cost for an attacker further. To date all the concepts I have sketched out have limitations I a find unacceptable but I believe there is a solution. Imagine if someday the hardware cost to attack the network was $5B but it also required another $50B in stake as well.