That would be a cool test as the beam exiting the GBall is not nearly as divergent as the raw emitters output, so you should find a sweet spot in the 3X BE where it does all it's focusing, kind of like how a G2 has a sweet spot.
I would empty out a 3E body and drill out the face or possibly cut it off and reduce the barrel length as needed with a dremmel, then just use the 3X and adaptor, just screw your hollowed out M9 x 0.5 (3E) barrel into the adaptor and check the length sticking out so that when you screw it into your 12mm copper module, you don't smash into the front of the GBall can, you should have a few mm to grab enough threads, it may even overlap it, I can check some GBalls I have loose and see if an emptied 3E barrel overlaps the GBall can.
----EDIT----
YES, you get about 2.5 mm of overlap, plus the GBall sits back in the 12mm copper module.
If you removed the inner sleeve past the threads of the 3E barrel then nothing would stop it overlapping all the way, but I doubt you need that much, I would open up the small end of the barrel.