If the backlash isn't too high, and the pinion seal is still good, no metal bits sitting in the housing, outside of an axle inspection with new seals bearings, new oil*. I might just clean it up and run it.
*(And of course, unless you are 100% focused on having two black stripes the same length...)
But then again, this is a full on resto, so maybe a complete?
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65 Laurentian post, 67 Grande Parisienne 4 door HT.
Run it. As you say, if you open it up and if it all looks good, if the axles look good, put in new axle seals, new oil and cover gasket and off you go.
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1966 Strato Chief 2 door, 427 4 speed, 45,000 original miles
1966 Grande Parisienne, 396 1 of 23 factory air cars (now converted to a "factory" 4 speed)
They are tough. The axles, not so much on the bearing surfaces.
At a minimum, new axle seals. That common leak at the tube to housing or spotweld, when it's cleaned up before paint, apply some sealer to those areas.
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65 Laurentian post, 67 Grande Parisienne 4 door HT.