This is not a hard-line fix to convergence, and to be honest, it's probably not even a "good" idea. It's more FOOD FOR THOUGHT than anything. Gotta keep those neurons and lasers firing

What if torso mounted weapons did not converge?
What if Each Weapon slot on your body was mapped to the silhouette of the crosshairs. For instance, the Dragon DRG-1N has an Energy slot on it's left torso, up high, as if on the shoulder. Instead of firing directly to the center of the screen, a weapon mounted here would fire slightly higher and to the left, with it's own little logo/icon. The closer an object is to the mech, the further away from the center of the screen the icon would be. This would make weapons mounted high up on shoulders less effective for fighting mechs smaller than you up close, but more effective when fighting larger mechs up close. Inversely, low-slung weapons would be better suited for smaller targets.
What if this didn't only apply to torso mounted weapons (and head mounts)... but also to weapons that are mounted to arm slots that lack lower arm actuators?
For instance, the Yen-Lo-Wang, when firing it's AC20 would fire slightly low and to the right of the crosshairs.
The idea of convergence makes me think about things such as this. Does the AC20 on a Hunchback HBK-4G articulate left and right? Was it "supposed to" in TT lore?
This is a kind of 'anti-solution' where in you further the effects of convergence on weapons, thus enlarging the awareness of a specific system, as opposed to an error.
However, this could very possibly be overly complicated. People might not like only being able to fire one side of their Jaegermech at a Raven within 180 meters. It might be EXTREMELY counter-intuitive for new players to pick up on. It might make the meta-game split even further, with people only picking from an even smaller pool of "viable" mechs with the right kind of slots.
This is by no means a SOLUTION. It's not even necessarily a "good" idea... it's just an idea. It might even be an interesting idea for some of you out there.
-Cormac