I have used Tightbond III for all my closed segmented work for years with no problems. Takes a little longer to dry but I'm not in a hurry. I use Tightbond Translucent for open segmented work
.Rarely does it require clean-up between the segments. I have never seen it in stores only online.
Also use a thin kerf saw blade, they are .10 thick. It starts to add up when you are making 48, 72 or more cuts.
48 cuts is 4.8 inches of waste plus 3 or 4 inches to hold for safety. So 48 segments will require almost 10 extra inches.