I am in a quilt ministry where we always tie our quilts. I am not a big fan of tying so, once I have stitched the outside and turned the quilt (so it looks like yours) I pin the entire quilt starting in the middle and then, using my walking foot, I start stitching from the middle out. Typically straight lines following the outside of the blocks.
I understand about your not wanting to quilt the middle of the block faces but if you use invisible thread it would be difficult to see and, in my opinion, a better alternative to tying, which is very visible. Plus it looks like you really only have about 3 that are large and would require a little more stitching than just around the outside. Whatever you decide on I know it will look awesome.
God bless you,
Kim