Improved initiators, solvents, and SO3 mixtures are disclosed which can increase the yields and efficiency of a process which converts methane gas into methane-sulfonic acid (MSA). MSA is valuable in its own right, or it can be processed to create desulfured fuels and other chemicals. Preferred initiators have been identified, comprising at least one “primary” initiator, and at least one “extender” (or secondary, supplemental, enhancing, tuning, tweaking, or similar terms) initiator. “Primary” initiator(s) include (unmethylated) Marshall's acid, mono-methyl-Marshall's acid, and di-methyl-Marshall's acid, while a secondary/extender initiator comprises methyl-Caro's acid, which can oxidize sulfur DI-oxide (an unwanted chain terminator) into sulfur TRI-oxide (an essential reagent). Other enhancements to the MSA manufacturing process also are described.