As an airline pilot who has been flying airliners for nearly 30 years I would like to make a few comments on the big differences between the pilot's experience of turbulence and the passenger's. I have no doubt that you found the experience very frightening. The fear of falling is natural and even airline pilots who are passengering feel that temporary sense of alarm when the plane suddenly drops. I wasn't there on your flight and I could be totally wrong but this is my opinion:
After a few minutes of this the turbulence went from mild to violent with the 747 being thrown around like I could never imagined. This started to make me a little uncomfortable, even as an experienced pilot and passenger, the seatbelt signs remained off and the cabin crew were still going about their business.
If the seatbelts signs were off and the cabin crew were still going about their business although it seems to you to be violent it is likely to have been nothing more than light turbulence. It is most unlikely that the pilots forgot to switch on the seat belt sign. It is more likely they judged it as light chop that did not merit the seat belt sign.
All of a sudden the 747 was flung violently upwards then slammed downwards as is if someone had hold of it by the tail. The engines had a clear loss of power and the aircraft went into a nose down attitude and began to bank right, all while still violently shaking, passengers screaming and trays drinks flung around the cabin. To be honest, I wasnt sure we were going to recover.
Turbulence does not cause the engines to lose power. If the airspeed suddenly increased the autothrottle would have commanded a reduction in power. Turbulence penetration speed is normally less than cruise speed and it is likely that the pilots selected a lower speed and the engines reduced thrust accordingly. Light to moderate turbulence will knock over drinks and trays with associated gasps from passengers. An abrupt change of 3 degress nose down feels like a steep dive to passengers.
The seatbelt signs went on as the flight crew tried to regain control of the aircraft and put power back onto the engines
The autopilot stays engaged in turbulence. Some aircraft have a turbulence mode where the priority is towards level flight rather than chasing an altitude. The flight crew would not be "trying to regain control of the aircraft" but would be allowing the autopilot to level the wings and the autothrottle to maintain a target airspeed. As the airspeed is likely to be up and down in turbulence it is likely the engine thrust will be too.
Incidentally if the aircraft experienced severe turbulence the flight crew are required to make an entry in the tech log. I've only had to do it twice in almost 30 years of flying. Severe turbulence does not normally last more than a few minutes. The turbulence you encountered may well have been unexpected. Pilots have weather charts with areas of forecast turbulence shown on them, but there are often areas with nothing shown that have unexpected turbulence.
I have been at a baggage carousel before in uniform waiting for my bag and heard a nearby passenger also waiting for his bag shouting excitedly into his phone that there was "unbelievable turbulence" and the plane "almost came apart". The turbulence was never more than light occasionally moderate and we had had the seatbelt signs on for about 20 minutes of the 8 hour flight. Of course he might have been on a different flight and been waiting for his bag at the wrong carousel but I doubt it.