As others have suggested, I carry around print-outs of the actual laws for WA state (my license is out of WA right now) for CDL requirements showing I am in the clear. I also have the FMCSA laws for the exemptions (private property transport), and I keep it with my insurance paperwork. I don't expect any of these guys to be trained up on the nuances of driving around a private party military vehicle with a guy on an out of state drivers license, I just don't. I also get it that we do have the hotshot situation and that's bringing up a certain level of enforcement (or revenue collection if you prefer, but you have to figure there ARE a lot of actual violators). OP's rig shouts hotshot. If some guy tried to write me wrong like OP here I would go for the supervisor on the basis. If I wound up with the tickets, then that's what court is for. Checks and balances. Sucks, but better than no recourse at all.
I haven't gotten pulled over in the LMTV yet, whether or not I had plates on it (I ran for a long time without because I was too lazy to do a mount - bad idea, just telling the truth). I blow all the scales whether or not I am legally supposed to go in (Like WA). I went in one time in WA early on as an experiment on I-90 and the guy was like, why are you here, military doesn't weigh. He thought I was Pvt. Dunce and my buddies in the motor pool had played a joke on me. I told him I was non-military private-party and he just sort of sighed and said don't bother coming in. I told him it was required and he literally eye-rolled - now I was Ned Flanders instead of Pvt Dunce - and waved me out. I think we have to realize that there's a pragmatic, practical attitude here regardless of the specific letter of the law, and that letter of the law did not have us in mind. These guys are mostly just trying to do their jobs to keep the roads safe. I've gotten lit into the scales (weigh in motion) and blown them anyways. I strongly suspect I roll by and they just make certain assumptions that I am military and who am I to dissuade them. NONE of this is advice.
I've driven unimogs around with no plates at all in western states and never had a problem. Maybe the attitudes is more revenue orientated in the east, I don't know. I've lived in VT and MA and certainly I can see that possibility. Out here (excepting California, which like Mass. is not America imo) if you get pulled over it seems like it's because they think the truck is cool and want to see it. I feel like I would have to drive a really, really, really long time in a M/V to actually encounter a problem.
I hear you all on the advice to stay silent but I just try to be reasonable when I interact at traffic stops (I've been pulled over many times in cars). You know don't say anything meaningful but don't silent treatment them either. Try to be friendly. Act helpfully stupid. A couple of encounters I've literally had to say the same sentence 10 times like I was autistic. "But I'm not commercial" "But I'm not commercial" "But I'm not commercial" etc. Just have a super simple story and stick to it. Show them the paper. Most cops are easygoing once they realize you are not going to shoot them. I've been pulled a couple times in Jeeps with a laundry list of issues (who has mudflaps, overhanging fenders, blah blah blah on their rock crawler) and the cops just sort of point it out but I've never been written for an equipment problem.
OP - you are doing the right thing, lawyer up, at least to the point it's non-moving. At that point it's just whatever's cheaper, fight it or not... I love NV, I got a ticket in vegas and they let me plead it down to a non-moving by bribing them ON THEIR OWN WEBSITE. It was a list of choices. God bless them.
No Cdl required 
