Aibohphobia
The MSI X99S Gaming 7 has a 3.0 x4 slot but I'm only getting 1400-1500. Is there maybe a newer revision that is faster?
I don't know. With your setup have you verified that the motherboard has it running at PCIe 3.0 speed? Only the slots piped directly into the CPU will use PCIe 3, the X99 chipset is stuck at PCIe 2.0. If you are using a 5820K with the decreased number of PCIe lanes, I have no idea how the routing would be handled either.
Looking at the manual for your board, the M.2 slot has a switch that links it to both the chipset and the CPU slot so I'm not entirely sure how that is supposed to connect and what decides where it switches to. I don't know how it can route to the chipset and remain PCIe 3.0 capable, basically you'd need to find out how that switch works exactly.
Edit: Found a PCIe Bandwidth table later in the manual. Did you enable or disable the "M.2 PCH strap" in your BIOS? Looks like it limits the M.2 to PCIe 2.0 if you have it enabled. With that off and only 1 or 2 GPUs installed then the M.2 slot is supposed to be PCIe 3.0. Installing 3 GPUs will force it to run off the PCH instead. Can't have any drives installed in the SATA 5 or SATA 6 port either.