Generally
First, you check code to be sure your requirements actually are what you presume them to be. I'm talking to you here.
Second, you talk to the AHJ and describe the problem and ask for a waiver. If you're having the problem, it is probably coming up on literally every job and they have an answer for it.
In fact, this reared its ugly head on an NEC revision that required a single disconnect switch. This had an unforeseen impact on 400A residential services, which are normally implemented as dual 200A breakers side by side. I think NFPA believed manufacturers would simply position the 200A breakers next to each other and come up with a $2 handle-tie... but this proved much more problematic than that. So states deleted the rule and/or AHJs simply said "keep using normal equipment this code cycle".
In your case
previous installer had hijacked ground as neutral to support a 220/120V oven on a 3-wire cable
Illegal using "/2+gnd" cable. Legal prior to 1996, but by no means safe, using "/3 no ground" (white neutral)... or "bare mesh neutral" SEU cable.
and was using a 40A breaker when the oven pigtail was only 12AWG
Actually, that's the one place in a house the "Tap Rules" are allowed to be used. Yeah, if the oven is good on a 20A circuit that's fine.
by running 12/3 Romex and replacing it (temporarily) with a 20A 2-pole breaker.
But-but-but- why not run 6/3 Romex and replace the entire -- Oh wait, I see what you did there.
Yeah. The oven needs the neutral, not the stovetop. (for reasons which are now dumb: the need to use "common everyday 120V incandescent bulbs that everyone has plenty of" as oven lights).
Now, whatever your old 40A range wiring is, that'll be fine for a no-neutral range. /2+gnd is legal for that. SEU can have its neutral converted to a ground. (NEC Chapter 3, SEU section). With "/3 no ground" you can destroy the white insulation and make it a ground.
My home is in a NEC 2020 state so it requires AFCI for pretty much all indoor circuits... I'd like to find a CAFI breaker for the oven circuit since I'm getting it inspected.
I'm all for people putting in AFCI breakers when they don't have to, to protect old wiring, particularly aluminum (which is perfectly safe when attached to terminals correctly; the problem is gold-standard practices in 1980 were very wrong).
"They're making us put AFCIs on everything!" is also great at the anti-big-government political rally.
However, your motivation is "to pass inspection". What matters is what Code says. In your case I can't find a darn thing that calls out AFCIs for 240V circuits in dwellings. There's a great deal about >>G<<FCIs for 240V circuits, and that actually creates a conflict... 2-pole GFCIs are common, 2-pole AFCI breakers exist in catalogs, but 2-pole GFCI+AFCI is a tall order. And NFPA is reluctant to mandate products which do not exist, but rather strident on their GFCI requirements... so I don't see them sacrificing those to get AFCI instead.