Accuracy comes from consistency. Having more freebore than necessary creates more opportunities for the bullet to develop inconsistencies in its path. It might engage the rifling at a slightly different point, or develop a bit of inertia in the wrong direction that isn't fully counteracted, or what have you. It's usually a very minor detriment to accuracy, and few people outside of benchrest shooters worry about excessive freebore.
Unless you go full retard with the fancy ammo, and make every round a saboted warhead with stabilizing fins, having all of your bullets tumble in flight will be an even greater accuracy detriment than anything freebore might cause. If all you're trying to do is avoid twist rate problems I think there are simpler solutions available. First, remember that for combat-level accuracy, your only real concern is under-stabilizing bullets, not over-stabilizing them. So if you have a very fast twist rate optimized for heavier bullets, it should still be able to shoot lighter bullets just fine. There will be a loss in accuracy, but not enough to concern the average grunt. If the mismatch is really excessive, it's possible that the jacket will separate from the bullet mid-flight, and the bullet will subsequently explode. I don't think you'll face any problems like that, but I don't know your project too well.
So let's say you do face an issue like that, with very light pistol bullets exploding when fired from the GPMG. There's a way around this in that, while people talk about twist rate matching up to bullet weight, that's not actually the necessary match. Twist rate matches up to the bullet's overall length–heavier bullets are longer, so people often use weight/twist rate comparisons to match up. So, if you just make the lightweight bullets of a similar length to the heavier ones–perhaps with a hollow pocket in the tip, not unlike 7n6–you would be able to avoid even the extremely niche exploding bullet problem. Also, listen to >>684642 , the Magyar brings up good points about headspacing and sealing the chamber.
What if you created a swinging-chamber design that sealed mechanically instead of using the cartridge? Say an O-ring on the chamber, plus a heavy spring pushing on it from the back. Alternatively, you could engineer a small lip on the barrel into which the chamber fits, and put the chamber on a cam track which forces it into the lip.