Is it valid to consider back-EMF in a DC motor equivalent to increased inductance?
Interesting.  The back-emf (modeled as a voltage source proportional to speed) is not equivalent to an inductance that depends on speed. Furthermore, there is no possible L(w) you can come up with that will make that assertion true.  

I will describe a simple experiment, but in essence I'll be saying that they can't be equivalent because upon a motor load change, an inductor dependent on speed L(w) will not affect the stationary state current (torque after all transients have died down, becoming a contradiction), while a voltage source dependent on speed v(w) will (which makes sense).

Assuming a DC motor, a simple proof is to imagine that the load on the motor gets reduced.  Because there is less load, the motor speeds up.  Also imagine we wait for some time so that all transients go away (t=inf.).  Now let's see what happens with both models: 

With the back-emf modeled as a voltage source, its voltage increases because speed increased.  This means that the current decreases, because the difference between the power voltage source and the back-emf voltage got smaller.  This means torque decreased, which makes sense because we reduced the load on the motor.

On the other hand, no matter what inductance value you give to the "back-emf inductor", the current on the motor would remain the same, because inductors are short-circuits in dc.  But this does not make sense, because torque is proportional to current and if the current remains the same, torque remains the same, but we started this analysis saying that we reduced the load on the motor.