The inserts won't have any effect on pressure. That will still be the same regardless of chamber wall thickness. Pressure may be a bit lower just ahead of the chamber because of the wider bore of the 16 gauge. However, the strain on the chamber walls will be considerably lower, after all you've just added the thickness of the insert wall to chamber wall. Not only that, you've also reduced chamber diameter which translates into less strain from any given pressure.
Nial