I will try putting a single card in each slot to see if there is an issue, but that doesn't seem to be the case because 2, 5 and 6 work and 4, 5 and 6 work, just with high temperatures. Could it be some BIOS setting I'm missing?
Definitely Yes, if the motherboard is running the GPUs with full x16 lane speeds with just two GPUs, the CPU on that board might not have enough available PCIe Lanes to support the third GPU.
Go to your BIOS settings and change the x16 slots lane speed to x1 and then try again.
EDIT: The power consumption for the GPUs is at 154W, instead it should be around 80-85 W for 30 MH/s Hashrate.
BIOS MOD (According to Memory Vendor) --> Overclock Memory and underclock core --> Undervolt core and memory voltages.
Then your temps will be around 50-55 while mining.
Moreover, keep a fixed fan speed rather than curve fan speed, it will improve the longevity of the GPU fans.