Can you post a picture of the quilt back, purplemem?
Adding another layer of fabric... even muslin will make the quilt heavier.
It would be a lot of work to take it apart and take the fleece out but it could be done if you wanted to save the quilt top. I've talked to quilters who have taken their quilt apart when they had a long arm quilter do a quilt for them and they didn't like the results....I would think it would be easier to take hand stitching out than machine stitching.