The 'level' bit isn't necessary for the forces to be in equilibrium. All that is required is that the vertical and horizontal velocities are constant. If you're going straight and climbing at 500ft/min then you are in equilibrium. You are only out of equilibrium when you are accelerating (either horizontally or vertically) e.g. when transitioning from straight flight to a climb.
So
That provided the foundation upon which to build the briefing on "climbing", where you MUST have a "Total Resultant" vector - otherwise there is NO climb.
isn't correct. (And I say that pulling my forelock because I dare say you're a far better pilot that I will ever be!)
B2B2: Bang-on right about the model (and why it doesn’t matter that much!)