How could MH370 fly west when satellite pings went east?
You have an error in one of your major premises.

You say "satellite pings went east".

That can't be derived from the data you have shown. The chart is showing Doppler shift. A westbound aircraft that is decelerating, or simply decreasing its component of velocity toward the satellite (by, for example, turning slightly southbound) will result in a change in the Doppler shift.

Deviations up and down on that chart don't correspond to the velocity being east or westbound, but accelerations towards or away from the satellite.