I have made 42 10' strip blocks by using muslin as a backing. My question now is: Do I join them as usual? If so does that make for too much extra material underneath? Or should I join them with strips sewn on top of the block--maybe zig-sag them together first?

You sew them like any other two blocks together, these seams will be a little bulkier.
You may want to use a little smaller stitch when sewing the blocks together and press them open :wink: :D:D:D

I do press my seams open on these blocks to reduce bulk.

yes I press seams open too. I am working on another strip quilt (sewing a few block when I get free time) - I am thinking I might use sashing on this one. Either way, I think looks good.