Correct me if I'm wrong, but if a an engine is producing 10,000lb of thrust, it would be consuming 0.01lb of dust per second ppm. Or 36lb per hour (16.36Kg).
600ppm would mean 9816kg per hour passing - and melting - through the engine.
Very wrong. You need to calculate the air flow through the engine. Nothing to do with thrust.
An example. Which I based upon figures from the Canadian VAAC, which seems to use a distinctly better model than the British one, with results divided in low, medium and high concentrations. Low goes from 10 to 100 micrograms per cubic meter of air. If you consider a plane flying at 180 m/s, an engine with a capture area of 3 square m, and a concentration corresponding to the upper limit of the "low" concentration, over ten minutes (an estimate of the time to cross a lower level cloud, after takeoff or before landing), you absorb roughly 0.3 grams of ash per engine.