I'll preface this comment by saying I used to spend many hundreds of thousands of dollars a year with BP for Castrol lubricants. I'm fully aware, first-hand, of how inept BP can be - especially their offshore finance team.
I'd suggest that an individual could apply for a sole trader ABN at no cost, put that on the AirBP application, and probably slide the application through. After all, you do run a business...Vanderlay Industries, was it? I doubt they're asking for P&L statements or anything for a small credit limit.
Yes, they're a bunch of idiots who are clearly out of touch with their customers in general aviation - but what did you expect from a huge company, anyway...