The Mississippi mud build up on those vehicles looks to be a task !
The 'mud' on my vehicles is reasonably accurate for the soil in NE Tennessee.
A few years ago, I asked my mother to get me some soil so I could match paint to it for my scenery efforts.
She sent me an big plastic jar filled with Stoney Creek dirt and some rocks.
Some of it is now on the layout and I had latex paint matched for the color which I used as a scenery base.
For standard paints for models, I've found that I had some paints which were a decent match.
Though the color of the soil would indicate strong magnetic activity due to iron ore 'rust' colors,
I used magnets and found nothing in the soil attracted to the magnet.
It's nothing like Georgia clay; that stuff is the worst.
I had to eventually throw away the BDUs I wore as a ROTC cadet,
that got dirty with that clay when I was going through training at Fort Benning,
no washing machine will get that stuff out all the way.
Still, my military vehicles might be more dirty than they'd be at a stateside unit during WW2.
Nonetheless, they seem to look right for the part.