Have you tried this method to reduce the bulk at the intersections?
http://greenfairyquilts.blogspot.com...lat-seams.html
It makes a world of difference in the thickness of the intersecting seams. I do mine this way all the time now. It takes a little longer, but is well worth it!
Alternatively, you could stitch a serpentine or wavy stitch back and forth over the seams and avoid the intersections. My machine has a serpentine stitch, but if yours doesn't you could just move the fabric back and forth to do the same.