If you have a trust, the trust can be approved to own an NFA firearm. You would simply be the trustee, authorized to possess the items. The trust route is slightly different than the Individual route. For starters, no need for the fingerprints, as a paper entity does not have any. Ditto with the passport photos. When you send in your paperwork, you will need to include a copy (COPY, not original) of the Declaration of Trust. With very little background checking to do (none?), the paperwork is usually approved quicker than individual transfers.
Now, how do you GET a trust? I'm glad you asked...
First off, a trust is an entity, not a corporation. There is no ongoing paperwork that must be filed to maintain a trust. There is no filing fee for a trust. There are no obligations whatsoever once the trust is formed. It exists, and that's enough. It has legal implications over the assets of the trust, as ownership is no longer in YOUR name, but in the trust.
Now that we know a little about what a trust is, here's what you'll need to do if you want to form one. While an attorney can draft up a perfectly suited trust, that may be unnecessary if all you are wanting is a legal method for transferring NFA firearms into your possession. If you wanted something MORE out of a trust, you should consult an attorney.
If you have determined you do not need professional legal advice, you WILL need some help. Socrates and Quicken both make software packages suited to estate planning, and include templates for wills and trusts.