ECC capable hardware tend to be very power hungry.

That's just an artifact of Intel disabling ECC on consumer processors.

There's no reason for ECC to have significantly higher power consumption. It's just an additional memory chip per stick and a tiny bit of additional logic on CPU side to calculate ECC.

If power consumption is the target, ECC is not a problem. I know firsthand that even old Xeon D servers can hit 25W full system idle. On AMD side 4850G has 8 cores and can hit sub 25W full system idle as well.

My HP 800 mini idles at 3W

Not always, HP Microserver n54l had support.