Current flow in long channel MOSFET in saturation
Your question could use some updating as it is not clear; however, if you have a "long channel" device, you are assuming that you do not have drain dependencies due to charge sharing at the drain/source edges.  Also, you do not have "pinch off" when you are less than threshold.  You have a barrier in subthreshold, so that the current will be completely dependent on the barrier height, as this is the nature of drift (subthreshold) operation of the device.



In the picture above, Psi_S is the surface potential, and the barrier is Phi_{SC}, so the current is fixed by Phi_{SC}.  The voltage you see at the drain will be decreased by the length of the device.  

The EKV model is uses pinchoff for the boundary between drift and diffusion transport, so I you really care about the effects of pinchoff, I would start there.

Alternatively, what you might be looking for is the effect of pinchoff at the drain.  The resistance of this region can be completely neglected for most purposes. You have a gate to substrate voltage to invert the channel, but the drain voltage will tie back into the channel edge and give you a "not quite" inverted region in the V_{ds} > V_{gs}-V_t.

I would sit down and start doing some band diagrams and the solution should come to you fairly quickly.