If your LPG is failing copper strip corrosion, there is sulfur present in the LPG. Copper strip corrosion detects the presence of H2S and elemental sulfur. Polysulfides can also cause the Copper strip corrosion test to fail. As the lead acetate paper was not black, then H2S and polysulfides are not the cause. Elemental sulfur can be formed at ambient conditions when oxygen, H2S and liquid water are in contact with one another.
If the problem is elemental sulfur, then caustic circulation rates are not the important factor. Find the source of oxygen and eliminate it. The H2S will then react with the caustic and the LPG should pass the Copper strip corrosion test.
Another sulfur compound that can cause LPG to fail the Copper strip corrosion test is COS. It will hydrolyze back to H2S and CO2 and the H2S will cause the Copper strip to fail. It can sometimes be difficult to detect this mechanism. To remove COS from the LPG, a stronger caustic is needed. Typically KOH in methanol is used to remove COS. Another method uses a primary amine, MEA, to remove the COS.
There are test procedures from UOP that will test for mercaptans and polysulfides.