From my understanding, the main issue is impaired synthesis of glycine due to impaired/suppressed? genes. if you have that, you'd have to dramatically reduce oxalates to the point where it causes other problems. smarter to supplement glycine.
From the looks of it, the increased consumption of glycine supplements won't affect oxalate. Yes, glycine/oxalate ratio would be improved, but this would not decrease the amounts of oxalate. So the associated problems related to the excess of oxalate would persist.