If the robot uses a stationary policy then the human is effectively solving a standard reinforcement learning problem. I therefore think it reasonable to assume that the human will be able to find a policy which is optimal with respect to any stationary policy taken by the robot, given sufficent time, as many standard reinforcement learning approaches have been proven to converge.

I think this is not a reasonable assumption. This is where most of the problem is (the cooperation part seems pretty easy if standard IRL already works for inferring goals). See: The easy goal inference problem is still hard, Model mis-specification and inverse reinforcement learning.