If I could just move things around however I felt? Well to be honest I think there are too many recipes in the hall of heroes, especially given how strong gunners are.

Padded Lines and Cowboy armor

I'd remove all of the new padded armor recipes from basil and swap them with all of the 3* cowboy sets. The cowboy sets start at 3* and are less suitable for new gunners, but nice for veteran players looking for interesting armors to try out. Another possibility would be to leave in some of the 5* armor recipes, like just the pure damage variations. That way, the armor with damage for guns vs a monster would be cheaper than the most often preferred armor that gave an overall boost. The player would likely be aware of these options when they got to 5* as well.

Iron slug

I'd move iron slug to basil, because iron slug is different from the rest of the magnus lines and by the time people are ready to branch in that direction, they're very capable of finding recipes and haven't been relying on the normal damage.

Autoguns

I'd swap blitz needle to basil and grim repeater to hall of heroes, because of its popularity and necessity when it comes to firestorm citadel. Requiring the player to go out of their way to get this thing would be good, and encouraging new players to get blitz needle early on is a shoddy practice when they're about to face up against the royal jelly and roarmulus twins, two levels where blitz needle is ineffective. Grim repeater and pepperbox on the other hand, would be nice weapons to hand off to players at that point in the game. I don't make the same distinction with tundrus and magnus because new players need a piercing weapon at hall of heroes, and magnus's normal hits (as the player likely doesn't have Seerus's mask/chaos/gun CTR) are sufficient for early play against beasts and fiends but less viable against slimes, which have higher health. Grim repeater on the other hand tears through slime's higher health like you wouldn't believe and is an excellent weapon to hand to newer players as it demonstrates the risk/reward mechanic of Spiral Knights incredibly well.

Alchemers

I'd consider moving one of the drivers/alchemers out of the hall of heroes as well, to diversify where they are found. Of the drivers, I'd probably choose hail driver, the least understood, as the utility it provides is underwhelming early on and magma, nova, and storm are all primarily nicer options for the early game. I'd also consider moving one of the alchemer lines to Krogmo's shop.. the haze bombs/brandishes are an interesting comparison that I'd like to make here- they're earned in all kinds of ways, and that makes the variety a bit more interesting than just having it all in one place. I'd probably choose to make magma driver Krogmo only, to encourage early coliseum play without having Krogmo end up as the "shock guy" as well as to differentiate it from nova driver. To compensate for these harder to get recipes as the ease of crafting alchemers is a small but noteworthy selling point and this would be something of a "nerf", I might consider making a new driver that dealt either curse at a disadvantage, or poison/stun regularly, or even a combination of statuses like shock and fire at the expense of more damage. The new alchemer line would be basil only.

The end result

The end result to all of this would be more potential if you found recipes, and more incentive to find recipes as time goes on. The other end result of this would be not finding some variation of sacred falcon bear sentinel firefly armor at T3 basil instead of the recipe you actually need, a practice that to me feels tedious and just downright bad. Of course, if there is a sword/bomb update on the way, it might make sense to leave the padded line in there for a while just to water down the what-you-want recipes.

In a nutshell-

At Basil only:
+Gunslinger cowboy items
+Iron slug
+Blitz needle
+Hail driver
+Possibly a new alchemer line

In Hall of Heroes:
+Padded armor lines (primarily no longer at Basil)
+Grim repeater

At Krogmo:
+Magma driver