Wow, that is actually an amazing performance curiousity adding parallelism to the mix. I guess this would depend on the M.2 spec?
So absolutely it is a network problem which means custom fiber?
I don't know enough about custom fiber to know whether that will help stretch past being network-bottlenecked — most NICs max out at 10 gigabits/second, but I've heard of faster ones. Eventually you might be able to make yourself disk-limited... Either way, backing up one file is probably easier than backing up a zillion files scattered around the filesystem.