If you're doing a pull through wood members and inside walls, you really don't have a choice unless you want to rip out your drywall and install conduit. So using NM-B is you're only choice.
You may use us a conductor rated for 95 amps with a 100 amp breaker in this application. In cases where the conductor rating is between breaker sizes, you may round up to the next size breaker as long as certain conditions are met. See NEC 240.4(B) or just ask any licensed electrician. I did.
Both estimates I have from contractors I didn't use both specified in their big using 2/3 NM-B with a 100 amp breaker.
No, you may not. Article 240 applies to the OCPD (breaker)
only. NEC 240.4(B) states "the next higher standard overcurrent device" (a/k/a breaker). However, 210.19(A)(1)(a) says, very specifically, that "the minimum branch-circuit conductor size shall have an allowable ampacity not less than the noncontinuous load plus 125 percent of the continuous load". There is no "next size up" exception for the conductors - only the breaker. For an 80A charging load, you require a conductor rated at 100A. A 95A rated conductor (NM-B 2/3) is an illegal installation. See this article for more information:
Mike Holt Conductor Sizing and Protection
Let's say you have an appliance - non-continuous - that has a minimum circuit size requirement of 95A. In this case you could use 2/3 NM-B to feed it, because the wire meets the 95A the appliance demands, but you would indeed protect it with a 100A breaker. In the case of the HPWC, you are required to have conductors rated at 100A (125% of 80A) because that's what the nameplate says.
This scenario is tested in every single code/license test that I've ever seen, because it's a fundamental building block for electricians. If your licensed electrician told you that 2/3 NM-B could be used for an application requiring 100A, you need to find a new electrician.
With #2 NM-B, you also run into some pretty serious bend radius issues. Southwire's 2/3 NM-B is 952 mils in diameter, so you need 4.76" bend radius just to accommodate it. It won't fit inside a 2x4 wall at all legally (because you can't legally make the bend for it to come out of the wall), and it won't fit inside a 2x6 wall without it being too dangerously close to the other side of the wall. Bend radius on NM-B cables are based upon the entire cable's diameter, while the bend radius on THHN-in-conduit is based on the individual conductor.
If you have one, let alone two, contractors who have provided estimates using #2 cable via NM-B, then either it's because you suggested/asked them to, or it's time to find a new contractor. It's a pain in the ass to deal with, my supply house doesn't even carry it without special order, and working it in closed walls is nearly impossible if you're paying attention to bend radius.
PS: When working in pre-existing walls with circuits this large, it's much easier to use liquidtight flexible non-metallic conduit. You can fish it without a problem, you can manage transitions out of the wall easily (because the conduit can be exposed on the surface - it means physical damage protection requirements), then once it's in place the wires flow pretty easily. I use rigid PVC in accessible, then transition using appropriate fittings to LFNC to deal with closed walls and other inaccessible areas (or just use LFNC everywhere, depending on run length). 356.30 allows for LFNC to be unsecured where fished, as long as it's supported properly at the top or bottom of the wall where you're installing.
