Dual-coil latching relay and diodes? Current on one route = latch, current on the other route = unlatch. Resistors to bring it down to the operating voltage. Should probably diagram it to see if it'd be that simple or not...
What about , instead of a switch, a slow DPST after the DPDT to eliminate the possibility of user error? Same latching mechanism as above perhaps?
Something like these? Though they seem to be ~10 ohms, might be hard to make fine adjustments:
AC power rheostat 110-220VAC 4000W open frame ACD-O220-4000
AC power rheostat with bias 110-220VAC 4000W with enclosure ACD-E220-4000L | eBay
They also mention "proper cooling", although don't define at what level of resistance you need what level of cooling. Clearly there's some point at which the heat sink alone would be sufficient, and some transition point where you'd need a fan.
I assume you mean neutral, not ground. In theory that shouldn't happen, but yes, breakers on all four wires is quite reasonable. Ideally I'd not want some gigantic breaker box-style breakers. I found these pushbutton ones:
AC 125V/250V 16A Red Reset Button Overload Protector Circuit Breaker 2Pcs | eBay
... but the trip times are awfully slow. I'd hate to have to use fuses and need to replace them if something goes wrong. Found some 15A ones that aren't slow, such as:
https://www.amazon.com/Zephyr-Circu...90665&sr=8-3&keywords=push+button+breaker+15a
There's also the issue that technically there's no requirement that all sockets be on 16A circuits. That said, "normal" sockets here generally are, and high-power appliances often assume that they are. For example, in my place, the only schukos not on 16A are in the kitchen (13A). And it's easy enough to check just by looking at the breaker panel.