Pilotboy,
You mentioned LA Harbour, which usually means San Pedro. However as an FYI one or two cruise lines leave Long Beach, which is 7-9 miles further.
I've used Primetime many times, but just personally prefer Supershuttle. Both can be irritating as heck, but since Supershuttle has a much larger market share, you seem to get out of the airport faster.
While I can not vouch for the $55 taxi fare to San Pedro, it might be a few dollars cheaper leaving from the Hilton Garden Inn, versus the airport. There is an city imposed airport fee that would be waived, and the hotel is probably $3 closer to your destination.