Ok, not to get involved in the belt washing is bad discussion, again...
I have an embroidered white belt. With the exception of the black fading to brown because of the use of bleach, I haven't noticed any distortion of the embroidery.
I kind of wonder how you lost 5 inches in the wash. I wash in cold water, hang-dry (assuming I wash my belt which I would never do
I work as an embroidery digitizer so I've had a lot of experience with the stuff. It's no more likely to get screwed up as it is if it were on a typical garment.