Ultimately, my view on this is that what you are asking for is a more consistently better double gunning experience, which sounds appealing, but may be fundamentally imbalanced.
Let's say that the damage potential / boarding success of any particular loadout can be graded on a scale of 1-7 (1 being the worst, 7 being the best). In fact, you could survey the community to get the perceived average range, then determine the low and high value to which the majority of respondents would fall in (lets say 60%). This assumes a bellcurve distribution.
Below is an example of what I think you would find if you surveyed the whole playerbase:
What I think you would find is that for sword and gun combos, the distribution would be tighter and would be more bell curve like, with most respondents replying that sword and gun are about a 4-5 in terms of effectiveness out of a possible 7. The average in this case would be close to 4.5/7. The tighter distribution makes sense. Sword is a lower skill ceiling, and there is less room to make mistakes swapping to a single gun, and reloading a single gun.
However, for different configurations of double gun, I would bet you the distribution is wider, and possibly even more bimodal, with 60% of respondents falling between 3-6 out of 7, and peaks closer to 3 and closer to 6, with less people thinking it is just average.
In this case though, the average is still 4.5, which means that it is 'balanced' but you have to remember that half of the respondents think it is actually worse than 4.5/7, and so will not use the weapon config. It also depends on where your natural ability lies. Good FPS player will probably view the loadout more favorably, and will take on roles more aligned with their skillset (boarders). This means double gunning is predominantly being used by those who view it on the higher end of the spectrum, raising the actual average proficiency in practice above the average for sword/gun.
The same could be said for sword/gun to an extent, but sword is largely viewed as the 'default' loadout, especially due to it's utility even outside of combat, and is more accessible for the average player.
Therefore, even though the perceived averages are the same, the wider distribution for double gun effectively means it is the better weapon composition in the right hands, i.e. it has a higher skill ceiling. This isn't all that surprising, but it has implications for balancing.
Buffing higher skill ceiling weapon loadouts tends to break balance more than buffing lower skill ceiling because, quite frankly, better players find new and better ways to counter new metas or create new ones. Double gunning is most effective in the hands of people who know the game inside and out, and have trained their aim in a multitude of more competitive shooters. They know the typical spawn points on ships to camp, know the ammo locations well, know how to animation cancel, know how much health the player has, and of course know how to aim well.
Adding weight to these guns, sometimes purposefully by making animations take a certain amount of time, or purposefully preventing fast switching is a design choice meant to curb what I call "hyper optimization." If you left balancing decisions to the best PvPers in the community, they would suggest changes that increase fluidity of combat because they ultimately are the ones who best perceive the inherent weight of animations. Everything feels sluggish to them because they exhibit the fastest reflexes, have trained their hand-eye coordination, and make use of every tool available to win.
They may make the recommendation because they truly believe the game will be better off with more fluid combat, but ultimately, they are biased. Not biased to make the game necessarily easier for them to dominate it. On the contrary, biased because they believe the game should offer more of a challenge by raising the skill ceiling higher.
To me, the inherent weightiness of guns IS the balancing force, and possibly should be even more weighty, not less. Increasing fluidity might make battles among high skill players more intense, but will actually make other battles significantly less intense and less fun when it comes to high skill players fighting lower skill players (which happens quite a lot!)
So I oppose anything that makes the high skill ceiling weapon loadouts, i.e. double gunning better, even if this change is targeted as a quality of life improvement / realism suggestion, it will make all guns better and therefore double gunning will likely gain the most from this. It is already used by the best players, and likely for good reason, and while the best players deserve to win, I don't think weapon loadouts should be changed to favor that without also seriously reconsidering how the game is marketed. Sea of Thieves is just not an E-sport title despite the various attempts to get it to become popular on Twitch and implement an arena mode. Maybe they could have been if they just listened to the hardcore crowd, but maybe the game also wouldn't be as popular as it is today in attracting new players.
I certainly support any change that makes reload / gun mechanics more consistent, i.e. fixing bugs and exploits like animation canceling that can hide evidence for how effective double gunning truly can be. Only then can the community properly assess if this weapon config is balanced. Until then, straight up buffs such as making things take less time overall / saving reload states because you chose to switch off weapon are just not something I support. There is plenty of evidence to rebalance other aspects of the game, including ships, but in my view, double gunning is already in a good spot, and might even be too strong.
