I'd assume the Blackbird's engine that converted into a ramjet once at supersonic speed had no moving parts at ramjet phase. If the engines were off, how then did it pressurize the cockpit at cruise altitude to ensure pilot safety and that he/she did not pass out from lack of oxygen?
The SR-71 used the P&W J58, which is full of moving parts, and works very similar to a typical jet engine. Your assumption that it has no moving parts is wrong. While the engine RPM did slow down at maximum speed (up to 90%), it never stopped, and always generated enough power for electrical systems, pressurization, hydraulics and any other needs.
While the cockpit was pressurized (but sometimes only to 26,000 ft. pressure-altitude), the two-man flight crew wore full body flight suits for warmth and oxygen.