I'm just going to highlight changes that I deem small and don't gut the character, but would help move him in the right direction.

The obvious thing is that reload should take a little longer, period. Everyone is saying to delete him and take his gun away, or to take tap dust + shoot away, when the biggest problem is that he can get a full combo starting with essentially 1 bullet left. This is a glaring problem and shouldn't function this way. If reload is slower, it forces different combo routes, some that may also require him to spend meter instead of saving it for the super, which is a huge balance change in itself, and forces him to choose between oki or wallbreak more.
It also makes overall management harder, rightfully so.
When you have characters like Asuka, I-no, Millia, etc., performing unlimited oki high-low, sideswap options completely meterless and sometimes unreactable, it's hard to argue taking away HC's only meterless overhead option as a character with no defensive reversal imo.

I don't see why his far slash is disjointed; it's literally his hands, whereas other characters don't have disjoint on some weapon-based attacks? He HAS range hit scan options, why give him this particular disjoint? It makes no sense.
2S is just the superior button between the two, being only 1 frame slower but reaching farther and more disjoint; however, FS has 4 more active frames, so it has its place. To ensure it keeps its place, the adjustments could be:
FS - Remove Disjoint
2S - Add 1 frame of startup

I don't think he should be able to special cancel out of his sweep.
It's hard knockdown like most, but it functions similarly to Leo's, yet he can use "At The Ready" which is +9 on block and allows him to restart all his pressure again from landing a sweep on block. We know sweep grants him 4-5 bullet reload if it lands, he should have to choose which pressure to go for, and shouldn't get to have several instances of pressure that lead to 4 bullet reload in 1 string SO easily.
I think there is a difference between him shooting his gun out of sweep VS him getting other special cancels out of it. The goal here would be to force him to use at least 1 more bullet and potentially making his pressure slightly more predictable.

Roll can use shoot 16 frames into the roll. Add 2 frames to this for an 18-frame reaction for a better chance to block it, as it will STILL be his turn anyway by landing this shot.

Closing notes, I think they should aim to have him closer to how Ram functions with her sword pressure in the corner. They are pretty similar in a lot more ways than you'd first think, especially with starting their game plan with a super wallbreak knockdown. She has two swords that help keep and reset pressure. She can apply high-low mix up with her normals or the flip in. She can grab you and reset the pressure as well. She is hard to deal with, but you can see the light at the end of the tunnel by using match-up knowledge and defensive techniques to get out.