My method of doing the Trip Around the World would sound confusing, but actually worked very well for me.
Instead of sewing together all the strips, (say there are 8 colors) then cutting, I would sew sets of 3 and 4 and alternate through the colors. When I was ready for a particular section, I did not have to remove stitching. I had them laid out on my cutting table and it worked well for me.
I made 3 Standard size and one Queen size quilts using this method and have another one planned.
June