How do I apply as a “Company” with a single member LLC?

Here is a good article that will hopefully help:

From a customer who just went through this:
The secret that unlocked the mighty door were these words as advised in the blog you sent me: “I want to convert my individual account to a company account.” She then took my DUNS number, stood by while I completed some online forms, waved her wand, and  PRESTO CHANGE-O, I now have an apple developer company account.