In my experience, at LAX they have no flexibility to sell you the top up miles unless you have the minimum that would qualify the purchase (70% I think). Not even 10 miles. I don't think they have any discretion as they call Hong Kong for anything related to miles. Departing Hong Kong they are often more flexible.
So try to purchase enough to have at least the 70% before you head to the airport. Be aware that the Starwood to Asia miles transfers can take weeks.