HOW CAN THIS HELP?
Would asking my customer to name his price help me sell DI in the non-standard market?...

As usual it is always best to tailor your approach to specific situations. If your customer is having difficulties obtaining Disability Insurance on the Standard market, chances are he is unfortunately in a high risk situation. eZ-DI specialized plans offer a unique and compelling solution for those cases! Premium levels however may be higher at the same Coverage - Benefit Amount to offset the risks and in some cases, your customer may hesitate.

WHAT IS DIFFERENT?
What is different about a name-your-price approach...

It first shows your customer the potential Coverage / Benefit Amount based on the premium level he or she can afford (or alternatively the premium level that would have been paid on the standard market). This approach in effect resets expectations as a prospect moves from the standard market to the non-standard market. The Benefit Amount will be smaller but it can certainly be a true lifeline in case of disability!