I had the same problem and asked a similar question in the AXI discord chat recently.
This is my own experience of what I did next, your mileage may vary - I encourage you to experiment
Just know that what you're trying to do is
genuinely hard. It does take practice, don't get discouraged early on
I didn't get much into Thargoid fighting previously. I only did it when Thargoids attacked the bubble, so I was really only interested in CZ's, not hunting Interceptors alone.
Originally I used a hybrid Chieftain that was
mostly like a knockoff AXI meta-ish build that used 2 class 3 AX Multis and 2 class 1 Gauss. That way I was able to get a decent feel for the ship whilst killing Scouts, and I tried to shoot the scouts with the Gauss as best I could, giving me practice targeting them (but also still being able to kill them with the Multi turrets

) in CZ's I just avoided the interceptors as much as possible or tried to use the NPC's as cover on attack runs, etc. Long story short, I only managed to partially kill one cyclops (assisted by the CZ NPC's who kept it busy) in
months of off-on AX combat and it was
incredibly hard and not fun. I mostly stuck to killing Scouts and running from Interceptors, a smart move IMO.
When the war started I decided to improve my Thargoid killing game, so I asked the same sort of question you posed here in AXI chat, from the advice I got there I did the following:
I built the exact AXI Chieftain. No homebrew, I did it to the letter. I watched a lot of AXI guides on how to fight interceptors. I was told that if you can practice with Cyclops fighting and get comfortable with it, you'll find CZ's much easier. I was hugely sceptical of this advice, but I kept it in mind and aimed to kill Cyclops' in a CZ instead of just the Scouts.
I took that Chieftain into AXCZ around ports in the warzones - the ports fire guns and can be used as cover, you can also dock at the port and get fixed up and re-armed without exiting the CZ area

Many of the Scouts also prioritise shooting the port instead of the AX pilots.
I went in with the intention of just surviving while killing only the scouts. Using Gauss against scouts
is hard, but if you learn how they move you can hold your shot until the right time (they slow a lot to change direction and often turn to present a larger target). Nail them with a full blast, it only take 1 full hit from all 4 Gauss on the AXI Chieftain and a partial second hit to kill a regular Scout, so really you only need to land 2 hits per Scout - less if the AX NPC's are helping, so I try to see who they're shooting and help them out rather than picking my own targets - at least at first.
That gave me a lot of experience in targeting with Gauss and staying alive in the CZ (using heat sinks, managing caustic damage, developing battlefield awareness of where the threats were coming from, etc, etc.) I also ended up duelling with the Thargon swarms a lot, learning to kill those using the flak launcher is a bit tricky at first but once you get the hang of it it's actually pretty easy - and getting rid of those dramatically increases your survivability.
After I felt comfortable doing all that (a couple of days pretty intense practice), I started attacking the Interceptors that come in and mostly ignoring the Scouts, just killing the ones that attacked me. I learned pretty quickly to spot a Cyclops from any other variant and just run from the others. Using my best impersonation of the AXI pilot masters - by that I mean literally trying everything they say from their training videos, using cold coasting, pumping heat sinks to stay cold, staying out of the engagement zone during certain phases, learning to trigger the field neutraliser at the right time, etc. I have now killed 4 Cyclops' in CZ's in the last 2 days - and did that while
also killing Scouts and generally staying alive (mostly).
I definitely did it really poorly. The first time I killed the Cyclops but died right after, the second one took ages, the third and fourth one I did in one CZ (repairing between at the station). I'm feeling much more confident about fighting Scouts
and Interceptors and CZ's in general - and the AXI people were right, learning to kill a Cyclops
does help killing Scouts with the same ship - because it's basically the same skills, aiming, resource management, combat awareness, etc.
Having the right ship-build
dramatically changed the experience for me. Going from my homebrew version of an AX ship to the AXI meta Chieftain was night-and-day. It's not just the guns, it's how the ship handles and gets on-target, how it manages heat buildup and the tools to cope in battles.
So that's my long-winded answer. The Multicannons are a stepping stone to using the Gauss. Focus on developing the skills to kill Interceptors. From there it's just practicing and refining technique and aiming. Obvs this will likely change and evolve though the war now anyway, so who knows what'll be round the corner
Hope this helps
Good Hunting!
o7