Hi!
What a pretty quilt!!
As a fairly new longarm quilter, that back would scare me, for a couple reasons.
1. are you wanting the backing centered on the quilt? The process of the longarm makes it difficult to do so, since all three layers are loaded separately.
2. is the backing at least 6 to 8" wider and longer than the quilt top?
3. Did you stabilize the terrycloth center with interfacing? If not and if the terrycloth material is stretchy, it could sag while on the frame and cause tension problems for the quilter or cause tucks from the sagging.
It's not impossible, but I would expect that the quilter may charge you more for the special backing and any issues.
Any other LA's have input? Jackie? Shelley?