Invent a couple "companies." Give them a web site and an important gloss of Serious Business. Have a couple friends or clients act as the contact point for the reference. Even more amusing: hire an offshore outsourcing company to act as the "human resources" department of your reference company. They should be under strict instructions to act very haughty with the recruiter, and tell them that "Mr. X" is far too busy to take their call, and to then sing your praises to the sky. Most recruiting drones will be quite satisfied with this encounter.
Recognize that they are only jumping through the hoops of their own corporate policy. Your hack is to grease this path for them and get that sweet, sweet money you desire.