I trimmed with scissors, I have some nice sharp Ghingers.
I had another thought last night - you could obviously leave your batting in situ behind the already quilted pieced tris, just trimming the batting to a quarter inch after joining to the unpieced ones.
Then put your long strip of batting behind the whole border. The result would be a double layer behind your pieced tries, and a single layer behind your trapuntoed plain tris. How does that sound?
For others not so far along, if you want to put long strips of batting behind the tri border, may I suggest you don't QAYG on the pieced tris.
I think I did it the hard way, but I didn't consider how I was going to get my tris together without sashing between them. In the end, it worked out fine, just slowed up production when I had to sew all those seams on the batting.