This ain't "armchair"; it's math; it doesn't care about what you want it to say. You wanna argue about weighting, fine, let's have a grownup discussion. Otherwise, go away, the adults are working here.
Spoken like somebody who has never been within 20 feet of a course on statistics and data analysis. Bad math is worse than no math, and how you analyze a set of data can have immense implications on the validity of your results. The math can't lie, but how you interpret and choose to apply it
can, because your interpretations and applications are fundamentally subjective.
To start with, your presumptions totally ignore the value of alpha strike weapons, and single-shot damage in general. A gun that deals 2000 damage every 1 seconds is better than one that deals 250 damage every 0.125 second, because the first will both have a higher damage rate in any real situation except the limiting case(consider a firing period of 2.5 seconds, the first fires 3 times the second 21, for 6000 vs 5250 damage dealt), and is easier to employ as it doesn't require constant aiming and is forgiving of short periods of no shot opportunities.
In Starsector, single-shot damage is also very important because of how it impacts armor penetration. The thread you linked actually goes into a lot of depth about what this means for many weapons.
Your hit calculation is doubly flawed because it ignores the huge effects of ITU/DTC which appears on many ships, and it presumes that combat always takes place at maximum weapon range. Trying to arbitrary categorize how important weapon range is in order to apply fixed factors is also not going to go anywhere useful. The utility of range is fundamentally not disentangleable from the weapon's performance both relative to other weapons(having the most range in a category has a lot more value than second-best), and relative to itself- a weapon with a lot of alpha threat is much more dangerous with long range.
There's no valuation mechanism for turret track rate or projectile velocity, which are in practice more important than weapon arcs in a lot of scenarios. Energy weapons get a significant edge out of this because they come with higher velocities than all but a few ballistic weapons, making them easier to hit with. This also ties in with how good a weapon is against different types of target- it matters less on bigger weapons or on ships that are roled around fighting capitals and cruisers.
OP value is not linear and should not be. Slots are a finite balancing resource on a ship, and therefore OP must have diminishing returns to scale for the same mounts in order to make slot restriction meaningful. Having things otherwise results in optimums being single high-OP weapons, which is problematic in balance terms. From an abstract perspective, there's also the reality that some weapons should simply be better than others. All weapons being the same flavor is boring gameplay, and if there aren't any meaningful decisions to be made there's no play to be had.
In general trying to separate weapon performance from their platforms is not going to work. Weapons don't exist in a vacuum and trying to balance them as if they do doesn't work. Yes, that precludes analyzing things with a simple spreadsheet. Life is hard. Using math to analyze complex systems is harder. Deal.
Looking at your sheet here's the major balance issues I see in it and why they exist. Gauss Cannon- high alpha, best range. Gauss is a very dangerous weapon and giving it decent relative flux stats is
insane. With 800 alpha it armor punches like a 200 damage HE weapon, so not actually half bad. Bad DPS does not fix the issue that a Gauss that doesn't have serious flux costs can eventually pick any ship apart at range with little risk of retaliation even if it slips up. Advancing its timing cycle makes it even better, so no. Just no.
Hellbore at 1600 HE alpha is nuts. It will take out nearly any armor in a single hit(only thing that resists is HA Onslaught, and even that loses most of its armor). 800 shield alpha is also not inconsiderable for any weapon. Sure, you pay in flux and DPS. Doesn't matter in practice because the threat of it will force raised shields even if not fired, and the damage dealt over a long time is less important than the big punch right now(and the HAG can't beat the Hellbore spikes until 15-20 seconds or so).
800 range on energy weapons. Not a good idea. High-tech ships are faster and have better flux stats. An Aurora could nose into HB range, fire off a shot to cause hard flux, and back of to let it vent. The other ship can't safely drop shields because the Aurora can sprint back in with it's high velocity and excellent against armor HB to punish them. And lower efficiency means that the Aurora is penalized if it does anything other than play in an extremely boring way or for a player fighting it, a frustrating one.
All of the medium kinetics except for Heavy Needler: Worthless. Flux efficiency is great. It doesn't compensate for not dealing credible amounts of damage. Soft flux can be dumped with shields up, hard flux from hitting the enemy can't be. Also the tradeoff for 100-200 extra range over LDAC is not worth it for a medium slot and much more OP.