so in my trust, i dont have an "assignment of property" document as you are talking about. my original trust was started with $5 (Texas law says the trust has to own something to be valid). after that, as i have added to it, i have created a one page sheet with the title "Amended Scehdule A to the Charger442 Trust". i add an item to it with the model number, serial and date of stamp approval and then i sign and date it. when i get the next items, i remove the old "Amended Schedule A" and create a new one with all the old info still on it, just with the new item and my signature and date.
i have always just updated my schedule A after the stamp was in hand.
i dont know if this helps you, but its what i do and its what i understand the laws to be here in Texas regarding NFA trusts.