Remember assumption 3: tanq @ q, so the paraxial ray angle is replaced by the ray slope. Now consider this macro: 

Macro does paraxial ray-tracing

This gives the result:

paraxial ray-tracing results

As the marginal ray angle set by the solve goes to zero, the paraxial marginal ray angle and tangent tend to each other. At this large marginal ray angle however, they are quite different.

To trace parabasal rays, trace a real ray very close to the chief ray and scale it to the desired pupil coordinate:

How to trace a parabasal ray

This gives

Ray-trace results

It can be seen that it is the parabasal marginal ray angle, or tangent of the paraxial marginal ray angle, that is set by the solve.