1. If the model is symmetric, why don't you cut it in half and only mesh the right side?
2. What do you care if the mesh is symmetric, as long as it is valid. You are going to perform a Mesh Refinement Study anyway, right?
3. There are times when you absolutely must have matching meshes, such as when using periodic symmetry, and for those special times, there is a mesh control to assure the meshes match perfectly. This does not seem to be one of those times.
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