Give OKW the MG-34 stock that is available from the HQ after any OKW truck is placed down and make the doctrinal MG a MG-42 and put it at 3cps or so. It'd hardly be OP given it's the worst MGs in the game.
The MG34 is actually not the worst MG in the game. That would be the .50cal, 280mp arriving way too late, and easy to de-crew. The MG34 cost 210mp and gets the job done. All things considered, I think that the MG34 is actually a pretty decent MG considering the price.
Though I like the idea of giving the OKW a non-doctrinal HMG, I must admit, that giving them a non-doctrinal HMG without doing anything about the fact that they have a super heavy non-doctrinal tank, 15 units compared to the other factions 14(UKF have 15 but will only at any given time in the game have 13 available). Not to mention all the other little bonuses they get, because they in the past had a resource penalty. So if these other issues with OKW get fixed, or you add the equivalent extra unit options to the other factions, then by all means add a HMG to the OKW. Till then I suggest players fill the gap with a commander as other factions are forced to do.