For all practical purposes, beams and cannons are essentially the same weapons, and the only real difference is the DPS potential that is based on the potential angle of attack. If your ship can turn quickly, then you put cannons on it so that you can do high burst damage, while beams are for the designated losers that cant turn quickly or cant mount cannons.
I would like to see beams and cannons split into wholly separate functional classes, so that they are strategic and not just chosen based on their DPS potential. Basically, I propose that cannons be converted into a pugilist weapon with greater hull-damage levels, but are unusable at range. In a combat scenario between an all-beam ship and an all-cannon ship, the beam ship should win most of the time if they can maintain +6k distance for the duration of the engagement, while the cannon ship should win most of the time if they can close and maintain -3k distance for a smaller window of opportunity. I am aware that there is already a damage drop-off at range, but I am proposing to go further so that the weapons have distinct functional purposes. This would promote more loadout diversity for general-purpose gameplay, and would also promote more specialized builds for team combat.
As to the accuracy part, the idea is that you have to get right on a moving target in order to hit it. This would reflect their ballistic nature--cannon fire is "thrown" at the target, and if the target is moving at all then it should have a much greater chance of missing. The simple thing to do here would be to simply cut the range of cannons to about 6k range, but I think there is room for a little more dynamic modeling. Lets say, a seed value of 100% chance-to-hit at 2k distance, with a drop-off to 10% chance-to-hit at 10k distance. The calculation should also reflect if either or both ships are moving, and the speed variance between them--if the attacker is parked and shooting at a static object then obviously it should have 100% chance-to-hit regardless of distance, but if the attacker and target are both moving fast then accuracy should go down quite a bit. Target size should also be a factor, and smaller targets should be harder to hit than large objects. All told, a fighter that moves around a lot would be much harder to hit with cannons versus a large lumbering battleship that did not have APO or EPtE.
To compensate for the loss of accuracy, cannon fire should have an inherent shield-bypass mechanism, something like 20% extra shield-penetration. This way, if you do make contact then you are guaranteed to do some pretty heavy hull damage.
One other change here, would be to remove the beam-only restriction on hard-points, unless they are balanced by other restricted hard-points (eg, cannon-only, torpedo-only, etc). If a cruiser wants to use cannons to punch up close, at the expense of doing damage from a distance, then let them do it.
There are a couple of other balance things that need to be looked at before this can be implemented, specifically changes to cloaking so that the attacker cannot sneak up right next to a target and unload into them from point-blank range. In fact I would not advocate this change at all without a lot of consideration and play-testing. Overall though, something like this would make beams and cannons tactically different, and not a default choice based on potential DPS alone. Captains would want to consider how both weapons would fit within a specific build and playbook, in the same way that they consider torpedoes and mines now. I suspect we would see a lot more diversity in the builds as a result, and a richer overall game environment.