Welding of Similar Stainless Steel with Different Sulphur Content

A fabrication unit welds machined type 304L stainless end plugs to type 304L stainless steel tubing approximately 10 mm in diameter and 0.5 mm wall thickness, using pure argon in a chamber and orbital autogenous Gas Tungsten Arc Welding (GTAW). There is a machined shoulder on the end plug, so it fits both inside the tube and against its end, with matching outer diameter measurements. When the sulfur contents of the two parts are different, the arc pulls strongly toward the low-S component, making it difficult to meet penetration requirements. It was not possible to increase heat input enough to make the difference without violating qualification limits. What’s causing this, and is there anything besides increasing heats that will help?