I do not really think I want to touch this with a 304.8cm pole, but I am not sure what the exact problem is.

Is the checkpoint order predetermined? If this is the case, it does not seem to be an optimization problem. There are enough constraints to define a unique trip plan using the maximum allowable rocket acceleration. What ever technique you have used for your current solution should be usable in the following successive approximation scheme.
  • Each checkpoint has a path which can be calculated.
  • From initial conditions for the rocket, assume maximum acceleration and an assumed meeting position with checkpoint one. If you arrive too early, try again with an earlier assumed meeting point. If too late, try again with a later assumed meeting point. Keep this up until you meet the checkpoint.
  • Now you have a new set of initial conditions for the rocket, and the same technique can be used to determine the meeting point with the second checkpoint.
  • And similarly for the third.
Is the problem to determine the checkpoint order which minimizes the time for the trip? If this is the case, why not just calculate for all permutations? Are there so many checkpoints that this is not feasible?