I wanna see the Mechwarrior who somehow replaces the whole barrel of his AC in-fight 
Instead of an ammo feed you have a barrel feed. Imagine a .50 cal machine gun, but instead of a big long belt of ammo, you have 5 barrels lined up on a track. One barrel is loaded at a time and empties its 10 150mm rounds in a second or two, then the empty barrel is cycled out of the firing position and a new one is slotted in and ready to fire in a few seconds.
Judging by how short AC/20s generally are in CBT, I'd guess that they actually are bulky because of how they are stacked inside the mech and around the actual firing port. They could theoretically have multiple barrels with a few shells each loaded into a cylinder array like a revolver, but they are all capable of being fired at once, creating a "wall of high explosive shells". Once emptied, the empty barrels drop back and a "quick loader" slots in 5 more loaded barrels for the next barrage.
This would appear to match the fluff on Sarna.net: An example of the rating system: the Crusher Super Heavy Cannon is a 150mm weapon firing ten shells per "round" while the Chemjet Gun is a 185mm weapon firing much slower (possibly 1 shell), and causing higher damage per shell. Despite their differences, both are classified as Autocannon/20s due to their damage output.
The Crusher may have something like 5 barrels tandem loaded for a total of 10 shells, while the Chemjet Gun might only have 1, 2, or 3 shells loaded up in a single larger barrel assembly.
Either way, plausible and pretty cool.