CMP was not on production line before 39' so it's out of competition. Praga ND and RV as trucks are in 35/38 time span but they lack AWD and after annexation any type of parts supply is out of question. Packard did not build trucks in that time span or I just unable to find one. Same with International, FMC only light ones.
That leaves:
Ford
American Bantam
Brockway
Caterpillar (outstanding)
Diamond T (also outstanding)
Federal *That's modern FMC
Freightliner *that's modern North American Daimler
Hayes Truck Company
International *You might know it now as Navistar.
MACK
Oshkosh
Studebaker (*Those 6x6s were unbreakable.)
and finally Willys (Jeeps)
All of them produced fair to goiod to excellent ATVS in the 1/2 to 4 tonne class in 1930s America. They had to. There was no good highway system outside the Boswash corridor or California before WW II. What passed for national roads in those days was semi-paved or gravelled. Europe had a better road network, though America had more and better cars.
1950s was when the country built a true highway system.
I have pretty large knowledge about quality of Russian equipment of that time. There is the Bad quality - Terrible quality - Soviet quality. Exactly in that order. The GAZ-AA and ZiS-5 of prewar production ware just abominations. They break just from looking at them.
That explains all the Studebaker two tonners still running around as prime movers for the Red Army doesn't it?
Speaking about CMP it lead me towards Scammell that is for sure interesting manufacturer.
That's Leyland, isn't it? Remember those lousy trucks that failed the British at Normandy? Guess who made them?"
German trucks ware not that bad, they ware even very good. Blitz was wonderful and tough truck but it was no good on any type of cross country driving. Mercedes-Benz L3000 was better in that role. Lancia 3Ro and FIAT-634N are also on table.
Lancia (Italy) worked better than it looked. Fiat was CRAP.
The main requirement I have is AWD and there is not too much competition in that department in 30's.
Look through the US list. Studebaker, International, Caterpillar, Diamond T and Willys in that order. If you must GMC Truck also.