Don't you think your relationship with said "customer" is going to be too cozy and hence not "real"?

Why don't you randomly offer half a months rebate to some percentage of your customers last month? (Also those who left you). Consider offer money as well as freebies (esp. for the former customers).

As you have a 10-day no questions refund policy also make sure, that you write clearly that it is a one time offer and totally okay if they don't wanna help..

I think you will learn more of that..