Maine Ladybug, perhaps the needleturn might not stand up to the washings this quilt is going to get, may I suggest satin stitch, although I donīt know how this will work on the blocks with several layers of fabrics, think you will need to cut the fabrics out at the back for that method.
Zig zag as well is good and if you have one of those posh Berninas I saw it had a double blanket stitch, could be the answer.