It is a federal approval, nothing speeds up the process that has changed little since it was implemented in the 30's. there is hope for the future as the ATF has a project to do all of this electronically.
Some say tax stamps for trust owned items are issued faster because there are no names and fingerprints to be checked. I doubt that theory is true since most of the wait is getting your application to the top of the huge stack on the reviewers desk. Plus, trusts are sent to the legal department to make sure they are valid.
I got my first can under an individual application. While I waited seven months for that to come back, I researched a trust and wrote my own using Quicken. After a few re writes to get it correct, I used it to apply for my second stamp, which has been pending 2 months so far. With the trust, I just need to make a new copy for each NFA item I want to apply for in the future.