Resurrecting this thread because I'm in the same boat. Want/need a quad M.2 NVMe in HHHL form factor. Cooling shouldn't be too much of an issue as I'll have a dedicated 13k RPM fan on the card like OP.
Only thing I've found is
Gigabyte CMT4034, and when I ordered a few new from Newegg, it was missing both the brackets and the black aluminum heatsink/shield so I returned them.
Next up on my list: jeyi iHyper M.2 PCIE4.0 X16 to 4X NVME Adapter Card PCIE4.0 GEN4 X16 to 4X NVME RAID Card PCI-E VROC Card
oh, now I remember why I struck that off: only supports 2280, need 22110.
This one's a solid
maybe (162mm long vs CMT4034 @ 150mm):
Linkreal PCIe X16 to 4 Port M.2 NVMe SSD Adapter-Low profile
Bit the bullet and ordered this one for a trial:
GLOTRENDS 4 Bay M.2 PCIe NVMe RAID Controller without PCIe Bifurcation Function, Support Intel VROC and AMD Ryzen Threadripper NVMe RAID, Full Aluminum Heatsink Cover
www.amazon.com