My Trust works basically the same. There is no 'Schedule A' or list of assets that is part of the body of the Trust. All ATF or my FFL sees when I add something is the Trust itself, The initial contribution I made when I set up the Trust, and an Assignment of Property form. The Assignment simply takes whatever item I own, and transfers ownership to the Trust. Lawyer says to include this form with a Form1/4 submission to establish that the Trust actually owns the firearm in question. The Assignment gets notarized and dropped in the files. The ATF Form 1/4 gets printed/copied when approved and also dropped into the files. I have seven eForm 1s and a paper Form 4 so far. Nary a hiccup.
Not all trusts are written the same, so your mileage may vary. What do the instructions that came with it say about adding an item?