I haven't actually decided how I'm going to finish my quilt off yet - but I've done a few sketches to show you some ways you might decide to quilt the negative space. I think this is a really great pattern to play with quilting negative space - there isn't so much that it is overwhelming, but there is enough room there to have a play with some large scale FMQ if that's what you choose to do.
Regardless of what you think you might like to do in the background, I would suggest printing out the colouring page at the back of the pattern (page 14 if you're making the lap size quilt) and doing some sketching. If I'm unsure about how I want to quilt an area, I always do this and have a play with different ideas. It's a good way to figure out whether something is going to work or not without having to unpick dodgy quilting, and you might find an idea you hadn't thought of.
1. Straight Line Quilting
I think quilting straight lines in the negative space would give a really nice contrast to all the FMQ in the coloured stripes. You could do horizontal lines, vertical lines, or lines that follow the zig zag pattern in the stripes - any of these options would look really great. Because there are seams through the background areas, you could use these as a guide to quilting too - which would make it a good way to try out FMQing straight lines.
With my first Giant Chevron quilt, I straight line quilted the whole quilt, following the chevron pattern. In the background, I alternated 1" spaced lines with 1/4" spaced lines and it gave the background a really great corduroy-like texture.
2. Creating more chevrons in the background
Another thing you could do is alternate different quilting designs through the negative space to create more chevron lines. I've alternated straight lines with curvy designs in this example, but you could do lots of different things. You could repeat some of the designs you've already quilted, or choose completely new designs (Leah Day has some fabulous designs and tutorials if you need some ideas).
3. An all-over quilting design
Another option would be to quilt an all-over design in the background. It could be a good space to try graffiti-style quilting (as in the bottom part of the sketch), and combine some of the designs you've used in the coloured stripes. Or you could do a straight-line based design to contrast with the quilting in the stripes. I really like the lines with circles idea - I'm thinking that's the kind of thing I'll do at this stage!
The options are pretty much endless - but hopefully these sketches have given you a few ideas for how you might like to approach it.
I'll be back with another post (on blocking and binding) after the holidays - probably in the first week of January. Have fun deciding on how you'll tackle the negative space :o)