A larger press is the ideal approach. You're not going to find a shorter broach.
We ran into the same problem this year. Our temporary fix was to create a secondary press platform below the one on the press (
we have one like this that lets us pass longer material through the bottom of the press.). We'd put the material on the secondary platofrm, press as far as we could go, then the broach would be far enough into the press that we could use the original platform to finish the job.
I hope I described that correctly. Just remember that if you do this, it's important to make sure your secondary platform is parallel to the original platform so you don't broach crooked.