If we assume efficient markets, it will drop significantly once you announce that you want to include a feature which worsens protection against double-spends
Also, I don't think you should depend on the fact that stake holders will be reluctant to participate in attacks which decrease exchange rate: "intuitively optimal" solutions can be very different from Nash equilibrium produced by independent rational players. I believe that double-spending with proof-of-stake can be quite like prisoner's dilemma where Nash equilibrium is the worst option. (Which, basically, means that one shouldn't include this feature.)
No. You forget that this is a stochastic process: number of signatures available in different forks is a random variable with large variance.
Attacker does not need to win all the time, he doesn't need to win most of the time. He needs to win from time to time.
Since variance is high from time to time his chain would win in a number of signatures and double-spend would be successful.
For example, if attacker has access to 25% of stake he'll get three signatures for three blocks in 1.5% of cases. So at least one double-spend per day.
Also note that legitimate stake holders do not always sign blocks immediately, they don't really have an incentive for it. Delayed signing will further shift probability towards attacker (stakeholders who work for attacker have higher motivation to sign ASAP).
Maybe. Its feasibility depends on particular economic conditions and altruism/laziness among stakeholders.
But why would you make your blockchain theoretically weaker? I really see no reason for it, it doesn't really prevent any kind of attack...