It doesn't seem impossible to me - 30kW seems high for lighting, a/c, etc., but I'm guessing that there might be enough heating and/or cooling capacity fitted to the coaches to make a them habitable within a few tens of minutes, rather than a few hours, after spending a below-freezing night or a sundrenched day powered down. That could reach that kind of power rating, especially with 1970s technology.
The extra 40kW for the kitchen car does feel like a lot, but *shrug*
Given that, an LNER set would need 8x30+70 = 310kW, plus whatever the power cars need when off, plus enough for the engine preheating that we were talking about... suddenly that 600Ax3 spec doesn't seem so unreasonable. There's still a question as to whether all of this needs to be done without any engines running - rather than just supplying enough for engine preheat and then having an engine power the rest.