What about the Himmelsstürmer? They qualify for the given technical specifics (if they aren't a hoax):
During World War II, Germany conducted late-war experiments by strapping two wearable shortened Schmidt pulse jet tubes of low thrust to the body of a pilot. The working principle was the same as the Argus As 014 pulse jet that powered the Fieseler Fi 103 flying bomb (more popularly known as the V-1 or buzz bomb), though the size was much smaller.
The device was called a Himmelstürmer ("sky stormer") and operated as follows: when the flier ignited both engines simultaneously the tubes began to pulse modulate. The angled rear tube strapped to the flier's back provided both lift and forward thrust while the chest-mounted deflector tube of lower thrust maintained a constant upward thrust. This lifted the flier up and forward. By opening the throttle to the rear tube, calculated "jumps" could be made of up to 60 metres (180 ft) at low altitudes (under 50 ft, 15 m). The tubes consumed very little fuel, but not much payload could be carried along either.
The device was intended to aid German engineer units to cross minefields, barbed wire obstacles, and bridgeless waters. The device was never intended for troop use.
The Himmelstürmer, never operated long enough to get extremely hot, and both tubes were angled away from the body of the flier. In operation the thrust difference between pulse tubes acted as a push/pull/lift system. Flight time for jumps was measured in seconds, with no lengthy descent time as altitude was minimal. As soon as the throttle was disengaged the device was shut off, a very simple operation, and there was no report of any casualties.