What dean said is right.

Sometimes the bottom of the dolls head hits the frame and causes the barrels to not fully seat on the water table. But, not often. If your barrels are fully seated and bolting closed and the rib extention still sits up some, it is because the frame that they came off of was not filed as deep as yours. The rib will need to be taken down, touched up and barrels refinished.

The joy of working on Parkers!

I've never seen a Parker where the bottom surface of the rib extension/dolls head comes close to bottoming out, as the rib extension isn't nearly as thick as the depth of the mating slot in the receiver. There is usually .025 to .030" of clearance between these two surfaces. Otherwise any debris such as dirt, bits of leaves, unburned powder, etc, would prevent the gun from closing. The dolls head has about 5 tapered vertical surfaces which are really the aligning surfaces, and these likely vary from gun to gun. A simple dye test, or smoke test will determine how well these surfaces mate up.
If the rib extension on the new set of barrels are firmly soldered in place, as Dean says, simple filing of the top, and re-engraving is the fix. However, the dolls head may not be going all the way down because of a vertical interference, and forcing it can tear the rib extension solder joint.
Anyway you shake it, it's a job for an experienced gunsmith.

Besides the fit of the barrels to the frame and the need to be a very close-tolerance fit - which is key to preventing premature wear and the resultant 'wiggle' - is the correct and equally close-tolerance fit of the doll's head extension. Not simply as a mechanical thing but for the proper aesthetic appearance. A doll's head that fits improperly is usually a dead giveaway that the barrels or the doll's head may have come from another gun. We have all seen them... doll's heads with .015" or as much as .030" or more gap between it and the recess it fits into.

Below is a doll's head illustrating a perfect factory fit.


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Rib extensions are not only soldered on but also screwed as well. That is what the ghosted circle is about 1" from the breech.

Allen, it would be best for you to send the second set of barrels to Brad for dressing of the doll's head. It will beat shipping it back and forth again.