Background: I am a deal lawyer. I'd like to think I'm good at my job. People pay me good money for this stuff, and I work regularly in a heavily regulated area. I do not claim any particular specialization in the NFA or in estate planning, though I have drafted more than my fair share of wills, revocable trusts, powers of attorney, and related documents for friends and acquaintences. I also have one NFA item on a trust, though that trust predates the 41F changes so the comparison is like apples to pears (closer than an orange, but still not the same).
The one thing that a trust definitely does better than anything else is take care of transfers post-death. While the NFA allows for a tax-free transfer of an NFA firearm to an immediate heir, and shelters a personal representative/executor from having to have its own tax stamp, there is still a form submitted to the ATF and they still have to issue a stamp. In other words, it's still a "transfer" within the meaning of the NFA, it's just a tax-exempt transfer.
With a trust, the stamp is issued to the entity, which is (in most modern jurisdictions) functionally immortal. As long as there is a trustee, a beneficiary, and some property held by the trust, it still exists -- so there is never a "transfer" and there never again needs to be a stamp.
I'll leave the questions of NFA consequences for someone else, but as a matter of trust law it is absolutely permissible (given appropriate language in the trust document) for a trustee to change the trust after formation. The 41F changes just made it so that the ATF has to sign off on the initial people responsible for the firearm -- but that change has no effect on the near thousand years of trust law that came before it.
As an aside, my personal read on the "constructive possession" issues to which Lobsterclaw alluded is that no, HH6 is not in illegal possession of an NFA firearm just from being in the house with your SBR. I would note, however, that there is a darned good argument to be made the other direction should someone ever decide to do so. One of the reasons I went the trust route was so that I could feel good about the wife knowing the combination to the safe without unintentionally committing a felony.
As I said before, this is a legal issue that requires a much more formal looking-into than can be had on an open forum. From the comments in this thread, it sounds like it's really an estate planning issue. NFA firearms are definitely a class of property that deserve special consideration in this regard, and I highly recommend that you find a good estate planning lawyer to talk through this with.