> you just need a valid interpolation between the identity matrix and the
> final transform matrix... which might take some sweat but is doable, as
> long as you restrict yourself to rotation and translation. (as long as
> the matrix is for a rigid transformation)
>
> Computes the axis of final rotation and the final angle.
> Apply the linear interpolation on the translation matrix, and generate a
> rotation matrix for the same axis and an interpolated angle.

Yeh, I think this amounts to pretty much the same as my first 
recommendation as quaternions describe rotations as an axis and angle. 
If the OP can calculate what the final orientation should be then this 
seems the easiest way.

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