It may well be a new development but I've found you can get an International Student Advantage card from here http://international.studentadvantage.com. I've read through the site and it seems you can be a student anywhere to qualify. Quote from their T&Cs:

"1. Eligibility
Members of the academic community (part time and full time students, undergraduates and graduates, international students visiting, studying or working in the U.S., staff, full time and part time faculty, and administrators) who are 16 years old or older are eligible to purchase the Card. "

I Heard back from Amtrak this afternoon and it's no problem to order the tickets from their website and then just pick them up at LAX. Reckon I'll be booking it up in the next few days.

Thanks again for all your assistance.

Simon