Sorry, another perfect spring day. I've never seen my local promenade by the beach so crowded...
Given your work, perhaps the best I can hope for is proving there is no solution.
Going back to the original point of this thread, I think it is more damaging to game physics (in terms of coming up with an orbit) that 1/2 a t² isn't respected. Gravity applies a change to the position as if acceleration were twice as high as it is while applying a change to the velocity vector as if acceleration is as written. You can't double integrate acceleration and get position, you can't take the second derivative of position (wrt time) and get acceleration.
While doing all of this I have now realized that a lot of my helper functions, written to work in the real world, do not work in Traveller LBB rules. An optimum intercept method (you want to have the same velocity and position of the target at the minimal time given some acceleration) that works in the real world doesn't work here.
My work above has all been presuming LBB rules, and I think there is still a geometric proof possible that will show no orbit is possible within the rules, but I think I've become a little disenchanted with LBB movement rules. Everyone can be expected to be able to work basic kinematics and the LBB movement rules were an unneeded abstraction.