AFCIs are also a bit like GFCIs in that they care a lot about crossed neutrals. A LOT. You will never get any AFCI to hold while a crossed neutral persists, nor should you! Remember, neutrals do not have breakers, the only thing that keeps them from overloading is the fact that they are fed from only one hot. If they are fed by 3 hots, one could return 45A and of course start a fire in the walls.
You will have to identify every outlet (including hardwired ones) on each circuit. Pull the covers off and the devices out. Document how they are wired. It is likely you will uncover the problem at that point.
If not, disconnect them all and light up each circuit, one at a time, to determine which is the "first" outlet. Hook up that outlet correctly (as opposed to how it is now) and test. Continue one at a time, thoroughly testing each time.
When you run out of things to hook up, and you still don't have problems, then you have licked it. Otherwise, the problem will return at a particular step. That is your problem area.
You seem sanguine about some crossed circuits in a 3-way light circuit. That may be one of your problems, and there may not be a legit way to regain original functionality without going to smart switches.
The 4x4 box right next to the service panel is a great idea, and I do that myself a lot.
Nobody cares which wiring method you use downstream of the AFCI.
Between the service panel and the AFCI, the inherent problem is the AFCI would never* detect a problem on that stretch of wire. That is a vulnerability, so that is where they require metal jacketed cable before the AFCI if the AFCI is not a breaker.
So, use a better wiring method. I have to say, for wiring between a panel and a very nearby box, EMT is faraway the easiest way to do that IMO. Keep it shorter than 2 feet, whcich eliminates the wire derate for 5 or more circuits. Ideally use 3/4 conduit, which has room for more than 10 wires and will give easier pulling.
Go to a metal 4x4 x 2-1/4 box, and use a 2-GFCI lid with 1/2" of lift. That will give you plenty of practical room to fit wires. If needed use an EMT nipple to chain to another 4x4 box. An arc fault inside this heavy metal is very unlikely to successfully start a fire.
Use THHN wire on through the conduit. If the circuit can't easily be moved to terminate in the box, come back into the service panel with THHN and splice there. This out-and-back-in method has 4 wires in the conduit per circuit, so watch your conduit fills.
* Actually, AFCIs do have some ability to detect arc faults immediately before them. We recently had a Siemens AFCI breaker faulting because it was clipped into a GE panel, and the clip/bus was not quite compatible.
Best Answer
We're reading tea leaves here to guess at NFPA's intent. NFPA writes the "model electrical code" which they offer for anyone in the world to adopt as their law.
But politically, NFPA has been having a big problem. Normally NEC changes are fairly trivial in cost: Pull a neutral wire on switch loops, gosh, you're using the /3 Romex instead of the /2. It's maybe $3 per house. Those increments have been getting bigger, as they've started so snake GFCIs and AFCIs in more and more places.
Mind you, AFCIs started out as a solution for electric blankets starting fires in bedding. However, they discovered that in actuality, AFCIs were catching arc faults caused by backstab connections. Backstabs are a builder favorite (jab a wire in a hole and you're done, instead of having to form a shepherd's hook and torque to spec, times say 200 connections in a typical house). Builders don't want to quit backstabs. (if they fail after closing, who cares?)
Well, in 2014, NFPA was hellbound and determined to require AFCI or GFCI breakers on darn near everything. And a lot of people were thinking "Why not just outlaw backstabs, then?" Anyway, NEC 2014 was adding six hundred bucks to the cost of a house, which was actually going to have a material effect on real estate prices.
Builders were saying "Oh hell no", and telling their Congresspeople to say "Oh hell no". And NFPA had to lobby right back, and influence public opinion. So states adopted NEC 2014 very reluctantly (seven still haven't), and some states still adopted it with some AFCI/GFCI requirements left out.
Anyway, requiring both AFCI and GFCI on a circuit was politically "a bridge too far".