It sounds like you have started a good foundation.
You really need to try to gain some big-band and musical theater experience as that is a big part of the gig.
You can start by volunteering to play for school musicals and regional musicals.
Sometimes you can volunteer to play for no credit at a local college big band even if you are not a student.
As well start listening and playing along to musical theater and big band. Check out Frank Sinatra with Count Basie and maybe the soundtracks to Chicago and 42nd street.
You can also work on ships by going on with a cover band or a jazz trio. You have to have a band and go through a cruise agency.
Good Luck Man! Feel free to ask if you need more help.
Cheers - Gabe
