Hmm, I wish I were more familiar with different machines, but I don't know how you could change that, if at all. I am sewing on a very economical Simplicity Quilters Classic myself and it does not do that reinforcing stitch. I can really see how that would be a pain in the butt!
I might try using a very fine needle when using that stitch to avoid the holes and maybe a fine thread as well, like a polyester or poly/cotton (unless you don't like those threads, many people don't). I'll be curious to follow up with this post and see how your problem is resolved! Good luck! ;)