Another thing to consider when designing omnidirectional weapons is recoil. With sufficiently high recoil, any weapon could damage the ship it's installed on. This would only be exacerbated by installing it on an omnidirectional mount. Traditional ships might be reinforced to withstand the forces from firing a weapon along the longitudinal axis, but firing such a weapon along the lateral axis might dislocate the weapon and collapse any internal compartments near it.
From this point of view, it shouldn't be possible for a ship to mount howitzers on an omnidirectional mount at all unless the ship itself was designed with omnidirectional howitzers in mind. There shouldn't be omnidirectional versions of howitzers at all, and all ships should have some kind of limit on the maximum recoil of weapons that they can install.
Instead of having higher level versions of howitzers that were modified to be mounted on an omnidirectional turret, there should be higher level versions of howitzers that were modified to be recoilless. Since this alone might not be enough to justify having a company sell a separate version of the weapon (or for the weapon to be a higher level), These recoilless upgrades would be paired with a swivel mount. The swivel mount would be limited by the extra bulk in the weapon design (not just mass but also volume).
I think that a balanced swivel limit for "omnidirectional" versions of weapon would be:
standard weapon -> omnidirectional/swivel version of weapon
----------------------------------------------------------------------
0 recoil at level(n) -> 0 recoil + 360 degree swivel at level(n+1)
1 recoil at level(n) -> 0 recoil + 180 degree swivel at level(n+1)
2 recoil at level(n) -> 0 recoil + 45 degree swivel at level(n+1)
3 recoil at level(n) -> 0 recoil + 20 degree swivel at level(n+1)
4 recoil at level(n) -> 0 recoil + 10 degree swivel at level(n+1)
5 recoil at level(n) -> 0 recoil + 7 degree swivel at level(n+1)
6 recoil at level(n) -> 0 recoil + 5 degree swivel at level(n+1)
Where the effective swivel value for weapons initially designed with recoil would be 360/(2 * recoil^2) since according to the
wiki entry on recoil:
The Wiki wrote:"The acceleration is proportional to the square of the [recoil] value"
There could also be tracking versions of weapons as an alternative to omnidirectional versions but balance aside; those would require much more effort from their manufacturers to design than sticking the weapon on an omnidirectional mount would.