ingame 'powered armor' 'deflectors' hull mods should bridge the gap, but they seem uninstallable at the moment. In the older versions, these were a rather strong, but somewhat costly inclusion that generally made rsf ships extremely competitive. Its hard to say what might be needed if these are working.
Most of the rsf seems to be built around the concept of surviving one engagement - the accelerated ammo feeders tend to provide a very substantial burst potential, but the mechanical limits of armor and the frankly sluggish fleet seem to counterbalance that. Additionally, rsf weapons tend to be short on magazine capacity (and thus, staying power) over other weapons, making the accelerated ammo feeders significantly reduce actual available combat time.
If the goal is to make them stand on the power of armor and reload burst windows, giving them enough speed to dictate engagements usually an answer, though speed in starfarer is generally stronger than any other stat overall. Their design is also somewhat that of a traditional slow but bulky fleet, so it doesnt really fit thematically much, but that isnt the worst thing. As mentioned though, armor tends to work better on bigger ships than smaller ones, perhaps this would only need to particularly affect the smaller ones. rsf ships using low flux weapons also tends to mean they get low flux speed boost (with skills) relatively easily, but this is still an investment just to make them 'work'.
I recall there was some work previously on alternate shield types, though I am not sure if any current mods implement them? Giving them a shield slot version of the dampener field for example would help extend armor's usefulness substantially. As mentioned, a repair system that feels functional and usable would go a long way, but I am not sure how to make that a reality. Maybe a sort of 'replacement armor plates' use limited system that repairs some large amount of armor instantly? This at least puts rsf ships in a place where they can take multiple engagements in a battle, then do a limited retreat to start a new engagement with those charges restored?
As for the weapons, making them rely on the rsf's integrated ammo feed system somehow is a bit heavy handed but possibly needed. This at least allows the flux costs to be the low overall, forcing the player to be picky about using non-rsf (and thus, flux heavy) guns on a flux limited ship. Improved magazine loading for ballistics is probably the ideal extra thing to include here, as it already mostly fits within lore. The issue of course is some other weapons (notably, the railguns) are actually pretty good on rsf ships already due to their ability to dictate space with the improved rate of fire and range.