the deeper part of the gouge is on the faceplate of the stem, which would be extremely easy (and likely quite cheap) to replace even if the bike shop doesn't buy your story.

I agree with HillRider that this isn't likely to fail - if one bolt fails, the other 3 bolts will still hold your handlebar and you'll have chance to replace it. And anyway, the stress on the faceplate is mainly compression from the allen bolt, not likely to cause that gouge to propagate. The smaller gouge on the stem-itself side is more of a danger because of the force on the threads, but that gouge is much smaller.