Please do continue with your letter asking for reconsideration. Be sure to place the highest emphasis on the fact that a genuine mistake was made, that no deception was intended.

Be sure to get the appeal done on time.

Start the ball rolling asap with an Immigration specialist/adviser/lawyer who has experience and knows the caselaw. You should be able to secure basic information on a free consulatation basis.

No need to fork out money just yet, just prepare and research whatever you can.
Wait for the consideration letter to be acted upon.