Just as a general update, I have taken the following measurements that I found to be particularly interesting. The distal third of the barrels are thinnest on the bottom of the barrels just before the chokes at .023-.024. The tops and sides of the barrels are much thicker. From the breach, measurements are (bottoms start at 4 inches):
1879 WW Greener Hammer Gun Wall thickness measurements
From Breach 2.75 4 6 9 12
Left Barrel
From Top 0.130 0.122 0.093 0.063 0.042
From Side 0.123 0.121 0.093 0.064 0.045
From Bottom 0.123 0.098 0.066 0.044
Right Barrel
From Top 0.117 0.115 0.091 0.064 0.045
From Side 0.116 0.120 0.091 0.064 0.045
From Bottom 0.128 0.097 0.068 0.044
Left Barrel
Bore 0.782
Choke 0.748 Full
Right Barrel
Bore 0.783
Choke 0.748 Full
I shot a round of trap with low pressure 10 gauge RST loads and experienced no issues. Given the above numbers, I think the gun would pass appropriate reproof, if subjected.