Thanks Jim! The cooling fan replacement is way quieter than the stock one.
Second, in case anyone finds this post in the hope of solving the noisy Lorex NVR, there has been some changes since the original post or maybe it's specific to my NVR (NR8081 included in the HDIP84W package). The PSU does still supply power (52v) for the internal POE switch and another wire to power the "motherboard" and hard drives, but the wire to the motherboard/hard drives do not use a PCIe 6-pin connector. It uses a 4 (1x4) pin connector and despite all my research, I could not find a name for it nor a molex adapter. I thought I had to go back to the old PSU, but I thought I'd try something...
I disconnected the PSU fan. It's no longer hardwired and I did not connect the wire to the internal POE switch. My guess is if the PSU wasn't drawing the power to power the POE switch, it should run cooler. Is there anything horribly wrong with my logic? It's been an hour and the PSU is warm to the touch. Granted, it's outside of the case for now, but I'll update this post when I put everything back together again and if I run into any trouble.