I never pushed the piston out, I just measured the depth of the piston from the face of the pump and the depth of the recess in the cover from the face of the cover. On all the covers I could see where the piston makes contact with the cover. I haven't got around to check and see how much more the piston can extend outward. I'm going to try get to it tonight.
Both the AAZ and LR pumps have dual springs with a small piston that has some grooves cut in the backside. 
Because of the different styles of pumps you'll have to use the shims in the stock cover in the new cover.
Spike - that is a weird looking dual-piston thing you got there. Definitely not like the '84 Jetta 1.6lTD pump.
Also, just today I pulled apart the timing advance mechanism on the '85 mitsubishi pickup Turbo-Diesel diesel-kiki pump (which is just sitting in my garage.

) It's just got the single piston and single spring like the '84 Jetta 1.6lTD.
I also did some measuring on it.

This one was easy to measure as it didn't have a manual cold start lever contraption on the back - just a flat block-off plate was back there. So I removed that plate. Behind there was, the back of the piston - and nothing else really interesting (no spring or anything.) I was able to push on the piston from the back to get it to move out. I found that it takes quite a bit of force to overcome the friction and get the piston to move. So this is probably why I wasn't able to get the piston on my '84 1.6lTD pump when I tried to "pull" it out.
I did some measuring on the mitsubishi pump pison travel specs:
max depth of piston: 8mm deep from front cover when pushed all the way back.
max protrusion of piston beyond cover plane: 2.5mm
So it was the cover that was limiting the max piston protrusion, and not something inside (until 2.5mm protrusion depth was reached, which seems to me like a pretty good amount!) This is very encouraging!

If our VW VE-pumps are anything like this one I just measured, we should be able to get significant advance with just this bolt-on cover!
Spike, how long until a production run on those covers? However long you say, I have a feeling it's going to be hard for me to wait.