My understanding is that AC-to-DC converters each have their own "sweet spot" in which they achieve their rated or advertised maximum efficiency.
Any device has a "sweet spot". This does not mean the design is terribly inefficient far outside of this sweet spot. In general, you can see that a typical AC-to-DC converter is passively cooled, there is no fan. From this it can be deduced that the maximum power loss is some watts at most.
For example, a modern power brick style AC-to-DC converter has practically zero losses when idle.
I want something with maximum efficiency at around 3 amps and 12 volts, but I'm having trouble searching for that.
Usually, the sweet spot is near the maximum load. You need 36 watts. I would pick (approximately) a 45-watt AC-DC converter with output voltage of 12 volts. Of course if you occasionally need more than 45 watts (3.75 amperes), pick a sturdier unit.