Calculating reflections
First of all, you wait for 5 tau for the transient to extinguish, provided that tau is the time constant of an exponential signal. When transmission lines are involved, the decay at each reflection is dependent on the reflection coefficient at the load and the generator. In general, you do not wait 5 line delays! (Consider the limiting case of a negligible impedance source driving a line terminated in an open or short circuit, where you have theoretically infinite ringing).

Then, as Ignacio explains, you can use superposition. Keep in mind that the solution for a constant signal is what you would obtain from classic circuit theory: the input and output ports collapse into lumped nodes. You can get the solution as a voltage divider. If you are able to compute vo(t) as the response to a unit step u(t), the response to A·u(t) is A·vo(t). And the response to a sum of inputs is the sum of their individual responses...