A theoretical and less important question is that were these few "allowed" companies main contractors to the Army and subcontracted from the other companies, or did each company supply direct to the Army. At least each small company seems to have had it's own WaA-inspector.
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Nice to see the seed growing.
Judging by the correspondence between the Heereswaffenamt and other military installations and manufacturers I have seen it was always direct contact to the manufacturers. So, to stick with examples, Polte did not manage the contracts, payment or deliveries of lets say P28 (DWM in Karlsruhe). So the designated "head companies" were not related to administration of the other ones in this business.