And 3-4 passes on a bomber formation is pretty much on the far end of what was actually done in reality. Much more likely was 2 passes max and then use all energy to go home before escort fighters catch you in a bad position.I am not sure it's question of being able to hit with the 360 rounds as it is combat persistence. Depending on wither you believe a "burst" is 2 seconds or 3 seconds (or another time) the 262 has 3 or 4 bursts before the lower cannon are out while a Spitfire has 4-6 bursts. A Tempest has even more and both are behind the P-51s and P-47s.
While many planes returned with guns unfired other planes either exhausted their ammo supply on one target or in a few cases engaged multiple targets. Yes it is more important for escorts but the 262 was good for 3-4 firing passes per flight on the bombers, then it is out of ammo.
Some American pilots managed multiple kills in their first combats, in part because they had 20-30 seconds of firing time.