Firstly, a short disclaimer: I believe that the 3 new Kuva Lich weapons are actually really fun and quite powerful weapons. However, the Kuva Hek seems to be lacking in terms of stopping power and comfort of use which leads to the purpose of this topic - to offer buff ideas for the Kuva Hek so it would be a more powerful and comfortable weapon to use than it currently is.
Secondly, I do not even believe that the Kuva Hek is an upgrade to the Vaykor Hek, just a side-grade at best or a slightly weaker version at worst.
The Warframe Wiki stat comparison of these two weapon variants is almost fully accurate to the game's stats aside from some errors (Kuva Hek has a reload time of 1.9 seconds in-game, not 2 seconds and it is not mentioned that it has a 0.3 punch through). Therefore, I will use most of the data from the Wiki as the basis of my argument keeping the inconsistencies in mind whilst relying more on the in-game data rather than purely basing my logic on the data provided on the Wiki page.
As we see in the comparison of both aforementioned weapons are quite similar in terms of performance, but there are a few differences that jump out:
The magazine of the Kuva Hek is 4 shots while the Vaykor Hek bolsters a magazine of 8 shots, yet the reload times are only 0.35 seconds apart.
The Vaykor Hek has a much higher potential power ceiling due to the riven disposition being 0.6 higher than Kuva Hek's. Sure, it is subject to change, but this still is an important factor to take into account.
The Vaykor Hek has a Justice effect which is quite useful due to its AoE factor.
The Vaykor Hek has a much faster fire rate (27.7% higher) than the Kuva Hek's.
The Kuva Hek has a punch through value of 0.3 helping slightly in clearing mobs of enemies. It cannot really compare to the Justice proc, though.
So for the solution of this problem: I believe that the Kuva Hek should have a reload time of 1.7 seconds or even a shorter one of 1.4 if we are being very generous. Personally, even with the reload time being at 1.4 seconds it felt quite sluggish because the weapon still has 4 shots and the fire rate isn't particularly high. Moreover, I will obviously mention that the Kuva Hek should definitely allow the usage of Scattering Justice. This matter should not even be up for debate at this point. Initially, I could see why Vaykor Hek would not have access to Scattering Justice due to it already having Justice procs (even then the logic fails in light of every other weapon example like the Dark Dagger weapon variants all having access to their mod Gleaming Blight mod) but the Kuva Hek not having access to it is absurd and should be remedied immediately because the weapon is definitely not in a state where it would suddenly spike to an overwhelming level of power with access to Scattering Justice, especially taking into account that multishot does not directly increase status chance anymore.
Reload time should be somewhere between 1.7 to 1.4 seconds.
Access to Scattering Justice should be granted to the Kuva Hek at the very least. Preferably all weapon variants should be able to access the mod.