How about this alternative.
UF-AC-41 " Velociraptor"
The AS-AC-18 is our most common weapon, but it has sadly become outdated. This new, modern variant is designed so that it can be integrated into any of our current designs that use it. It follows the same design principles as previous iterations of the guns, but thanks to modern technology and materials we have made great progress. Better springs, bolts, timing all allow great performance improvements. Fire rate is increased drastically, up to 800 rounds per minute. Muzzle velocity also increases by 25%-50%. In addition all our ammunition has been carefully re-balanced to ensure that all ammo types can be fired from the same gun without recalibration.
Are you trying to accomplish this with the same caliber and action? A hotter powder load might get you your muzzle velocity but increase recoil. As for interchangeability of ammo types, you'll probably have to give up the advanced primer ignition which will make the whole gun significantly heavier (and be a different gun). In fact, even increasing the rate of fire and muzzle velocity at the same time will mean the gun must be heavier; an unfortunate principle of the API design.
I must say, you're wrong on this.
The German MK108 cannon used mixed belts of Incendiary and explosive ammunition, and it was an APIB operated gun. APIB only has an issue if one bullets weights a lot more than the other.
http://www.luft46.com/armament/mk108.htmlI also found a manual for the Oerlikon 20 mm autocannon, which also used APIB. It to has several ammunition types, with no need to recalibrate the gun to switch between them.
http://www.forgottenweapons.com/wp-content/uploads/manuals/oerlikon_manual.pdfThe MG FF could fire AP, HE, Incendiaries and tracers. Only minegeschoss was a problem. Given that we don't have those rounds.
https://en.m.wikipedia.org/wiki/MG_FF_cannonAbout weight and firerate, the facts are different too. The Hispano-Suiza HS.404 fires larger cartridges than our gun, at higher firerates, with higher muzzle velocity and it weights just 40 kg.
So, it's clearly possible to build a gun without APIB that isn't heavier than our current autocannon.
Given the that the APIB design allows for higher firerates with less weight in the guns, upgrading our current cannon to the standards mentioned in the post should be very feasible.
https://en.wikipedia.org/wiki/Hispano-Suiza_HS.404