I'm definitely not the expert since I don't hold an FFL and don't keep up with every single change that comes out. That being said, I understand the process fairly well (or at least think I do).

The link above helps explain it to FFLs that don't understand the process. The other bit of info that helps is from the current 4473 (that's been required to be used since mid-Jan). The key to the whole thing is that the person doesn't require a background check. Prior to the new 4473, the last time the ATF addressed NICS checks for trustees was 2008, and they said it didn't have to be done. The new 4473 says:

A NICS check must be conducted if an NFA firearm has been approved for transfer to a trust, or to a legal entity such as a corporation, and no background check was conducted as part of the NFA approval process on the individual who will receive the firearm. Individuals who have undergone a background check during the NFA application process are listed on the approved NFA transfer form.

So, no NICS check required for post-41F submissions, as the ATF has already handled it. It now spells out that pre-41F submissions would require a check. However, in a lot of states (mine, NC, being one) your CHP/CWP/CCP/whatever becomes the exception to the check. There's a documented process to mail the 4473 back and forth and for the dealer to notify the Sheriff.

OP...provide the document GB128 linked and point out the Instruction for Questions 20 & 21 on the 4473. Assuming your state doesn't require a NICS check if you have your carry permit, or for some other reason, you should be able to have the suppressor mailed to you. I know I talked to a guy in CO that couldn't do it because they require a NICS check regardless of the circumstances.

Agreed. It's a very small window of time that it's even up for discussion.

Unfortunately, I can't imagine many dealers reading 27 CFR 478.102(d) and having that overrule the instruction snippet I posted...even if it's the correct thing to do.

I told the one dealer that said he couldn't do it (he said I had to be a Class III dealer to receive it) that there's a difference in what he couldn't do and what he wouldn't do, and that of choose to take my future business elsewhere.

Could be a store policy, or just simple ignorance of the law...but I don't have a use for dealers like that for either reason. Now, if it's a legal issue like it is in some states, that's a whole different ballgame, but all dealers in the area should be refusing to do it if that's the case.