A good point my friend: and in truth I think the answer to MG34/41 is “yes”.
In 1978 I had a very large book in my hands, which detailed the histories of most firearms that had been produced from about 1800 through to 1977. It weighed a good 15kg as a softback, was about 40cm tall, 30cm wide, and 12cm thick.
It was about $120. at the time, and I never bought it: these days it would likely be illegal to even own it, in politically correct and thus backward NZ.
The section on the MG34/MG42 was about 25 pages. From memory the MG34/41 was full auto only, and ran at 1100 rds-per-min, which would tie-in with the figure you mention in your post. Again, from memory very few (comparatively) were manufactured, as they were an interim weapon pending the service introduction of the MG42.
I wish I could recall more, but I hope the above data helps you, PK.
Kind Regards, Uyraell.