I am no B737 expert either, however, there are a few of slightly incorrect assumptions being made here.
markjoy said, "...At that point the EEC detected the thrust lever mismatch and disconnected...". I don't know that any EEC would do this. Each engine has it's own EEC and they work quite independently so would not do anything in the case of a thrust lever mismatch.
Maybe you're talking about the Autothrottle? As Avid Aviator says, "All the A/T ever does is move the thrust levers.". Quite correct. The EEC is the computer that sits between the thrust lever and engine and tries to get the engine to do what the thrust lever is commanding, regardless of whether the autothrottle is commanding the thrust or the pilot.
The autothrottle (when engaged in the cruise situation) would have been moving the thrust levers to command a particular speed. When actual speed goes down below commanded speed, the autothrottle pushes thrust levers forward to regain the commanded speed. In cruise this is not particularly aggressive as this results in an uneconomical fuel burn i.e. if actual speed is M.01 below commanded speed, the A/T does not "pour on the coals" but gently increases thrust. It would be more aggressive if the speed shortfall was larger.
The fuel flow that results from a particular physical thrust lever setting will be determined not just by the actual thrust lever position but also by aircraft weight, centre of gravity, altitude, temperature and airspeed. EEC's can, and do, fail of course (despite what bushy says!). In fact aircraft can be dispatched with EECs inoperative (just be careful firewalling those thrust levers!). I am not sure if there were any problems with the EEC as a result of the engine spitting a blade in this case, however anecdotal evidence would suggest there was not.
Not trying to be anal, just be careful with your assumptions.
To answer the original post about why the vibration reduced when they reduced thrust, here is an analogy. Turn your pushbike upside down in the garage and spin the wheel really fast. All good? Now stop the wheel and give the wheel in question a few nice belts with a big mallet. Spin the wheel really fast and the bike will shudder like buggery and probably fall over, however spin the wheel slowly and it won't actually vibrate that much. Apply the same principle to a series of big metal discs rotating at tens of thousands of RPM in an engine being forced to turn by combusting fuel and air. When an engine is brought back to idle it is, essentially though not quite, windmilling so the vibration would have decreased by a substantial amount.
The whole reason the autothrottle would have been disconnected by the crew is to reduce the vibration and although this action reduced the vibration it made subsequent diagnosis of the problem more difficult as the problem appeared to go away. Believe me, it comes as quite a shock when this sort of thing happens - lots of noise, vibration, calls from the cabin crew etc etc.
It would appear there were a number of other factors contributing such as: limited and therefore possibly inadequate conversion training for pilots, both pilots limited experience on type and poor design of engine instrumentation. I recall the captain was interrupted by a radio call as he was about to review their decision to shut down the "wrong" engine and subsequently did not complete the decision making process.
This particular variant of the CFM engine was not tested in all flight envelopes (combinations of airspeed and altitude) prior to entry to service and subsequent to this accident more stringent certification requirements (as far as testing goes anyway) were introduced for engines.
With the benefit of 20/20 hindsight (!), lessons learned are.... Sit on your hands unless you are on fire or about to hit hill, don't let ATC rush you, use ALL the information available to you to make a decision and when you've made a decision, go back and review that facts and figures to make sure you did in fact make the right decision.
Safe flying people.