Have you tried wrapping the body after the binding is glued / taped up ? I now use my trusty MTB innertube split and tied into a long length. It adds flexible clamping pressure , wont stick to wood glue and tightens up all the little gaps that tape alone just wont get. I just bound a uke with outstanding results...absolutely no filler required anywhere, and that is a forst for me!!
You may want to check out luthier tips du jour on you tube, Robbie uses a very similar method when binding his guitar bodies and as always his vids are full of useful stuff.
here's the link
https://www.youtube.com/watch?v=6haG-aDM-eg" onclick="window.open(this.href);return false;