Power them from a pure sine wave inverter connected to a battery thats being charged. Aka a good UPS
Typically the Ethernet shield is also only alibi-insulated from the device's ground. Sometimes not at all. (Personally it's always funny to me to see the fat 1kV/1nF capacitor from the shield to the device ground and then the metal of the socket is just bunched up with basically no clearance against the metal case or something like that). This can of course be avoided by simply using unshielded cable.
It takes an awful lot of power to smash through these multiple layers of insulation and bypass all the capacitors, at least if the PSU is properly designed (specifically, clearance between the various power / ground domains).
In contrast, Ethernet transformers are tiny small little things.