Batting too thin for purpose. Anything I can do after I've already done the quilting?

I'm making a quilted bag. So far I've made a few phone bags and now I'm making more of a hand bag. The problem is, I used only one layer of batting. This worked just fine for a mostly flat phone bag, but it's too flimsy for a bag with 2 inches of depth. I only realised after I started sewing the seams and it started to look like a bag.

I'm still a beginner so I'm not sure what I can successfully do to make the bag more rigid. I also really don't want to start over or pick the quilting stitches out​. It took me all day to quilt diamonds (criss crossing lines), and the bag needs to be done by Sunday (it's a gift). ​

I have two ideas. Quilt another piece of batting with basic straight stitches just to keep it together (with or without a layer of fabric attached?), put it with the original piece and sew along the edges to attach them. I worry that this might have some weird sagging effect though where it's not attached through the centre? My other idea is to try interfacing, but I've never used it, so I don't know if that would work on batting instead of fabric, or what kind I should get (fusible or sew in?).