Have you looked at the Source Diode? I think it would give you all the controls you're looking for more directly than the Source Ellipse. You'd leave the Gx, Gy values as 1.0 so as to keep your standard Gaussian distribution, but then use the alpha terms to set your divergence.

The only trick you'd need to use is if it's important to have a circular/elliptical emitting area, then you could use an absorbing Annulus object right after the rays are emitted from the rectangular region to change the emitting area from rectangular to elliptical.

The Source Gaussian may also do the trick, if your beam is circular (not elliptical), which it sounds to be.

Thanks this helps!  I was unclear in my first question. I actually have two different M2 values and two different divergences, one pair for the x-direction and one pair for the y-direction, so using the absorbing annulus object will be helpful.  I ended up figuring out how to modify the source ellipse to better fit my actual laser source, but after reading up on the source diode, I think that it is easily the better source to start with.