How about the middle ground solution:
I seriously doubt that an AEG style GL would provide sufficient power, your best bet would probably be self containted gas charged shells. The ideal one would probably be those recently posted Mad Max shotgun shells (5 8mm BBs each, right? Could probably mod it to shoot slug or a lot more 6mm). They're smaller than the 27mm moscarts (so closer to the real 20mm) but also pack quite a bit of power. Next best, external gas. Lord knows there's enough room in the OICW to cram a tank somewhere
. Still, this system is rather overly complicated but at least an example already exists in the M1100.
How about an electronic load/fire/extraction system for selfcontainted shells? It doesn't seem too difficult to do, and is easy to intergrate with the rifle section's electronics. You'd basically just need a AEG style mechanism, only instead of drawing a piston, it'd move the bolt to load/extract.
Also, just on accurate replication, the battery would have to be in the rifle, not the GL. Afterall, the rifle section can function standalone, while the GL can't.