Yes you can! Amos seems like we have been through the same fiasco.
Fortunately the Ecocash switch is much easier than the change of ownership. Here is what you do.
Copy of your ID, Old phone number and new phone number. Fill out a new Ecocash form at any Econet store and explain you are moving your ecocash to different number. The econet staff will make a note that this is an amendment and will process within 30 minutes.
p.s If it is close enough to you I highly recommend Econet 7th and Livingstone.