Mark, you say that you meet all the requirements apart from the licence, but the website clearly states that in order to be considered, you require >500 hours on aircraft greater than 12,500 kgs MTOW. Last time I checked, the B1900 was around half that?
Given that you don't meet their stated minimums in terms of either
1. Holding an ICAO ATPL or JAA FATPL
2. Having the required 1500 hours total time
3. Having 500 hours on any aircraft that's big enough to meet their requirements
4. Preferably having jet experience, glass cockpit
... my guess would be that you're sh!t out of luck mate
I do wonder about your authenticity to be honest, since when exactly did Eagle start taking on 400-total-hours pilots into the B1900?