I opened up the DPSS head yesterday and tried adding the 3element 405 glass lens in various places, but didn't get any satisfactory results. There is a very limited amount of space inside the head for which to mount an additional lens. I don't have the capability to drill out and tap the main aperture to insert the aixiz lens assembly (I'm in an apartment, with only hand tools, no power tools), so I'll look into some external corrective lenses.
As far as using the aixiz lens, at best I was able to get a TEM30 beam with even worse divergence, but the output was definitely brighter. I figured out why as well; inside the head the last stage before the lenses is a non linear crystal inside a plastic housing. This crystal is on a TEC by the way. Anyway, the plastic housing had a small square about 6mm x 6mm with a tiny hole poked through it over the aperture. After removing the square I noticed it is what looks to be a piece of chinese soda can, flattened out. You could see the chinese writing on it. When I removed the pinhole sheet and placed the 3 element lens in front it must have focused in a lot of what the sheet was blocking, enough to clear all apertures/lenses, thus increasing output slightly. The TEM30 beam was ugly and the lens actually made the divergence worse, so I ended up removing it and putting everything back where it belonged, minus the soda can pin hole.
I ended up trying my hand at realigning the nonlinear crystal (with proper IR laser protection on!) but couldn't get it any better than the way you had it, so I put it back where it was and closed it up. My hat is off to you on your realignment job, really well done.
Glad I opened her up anyway though, much brighter without the soda-can-collimator!