From my experence building stacker trailers, seems to me the DOT required 2 5/16" balls on trailers over 7,500 GVW. That's why they might be scarce. However as stated above you should be able to find one with a 1" shank which should suffice.
This was trailer Ser #100 we built in 2000 before I sold my interest in the plant:
http://i4.photobucket.com/albums/y12...ailerAlone.jpg
It had a 13,300 GVW with 1,650#'s on the ball.
Dry