Improved initiators, solvents, and SO3 mixtures are disclosed herein, which can increase the yields and efficiency of a chemical manufacturing process which uses a radical chain reaction to convert methane (CH4), which is a gas under any normal conditions, into methane-sulfonic acid (MSA), a liquid. MSA is useful and valuable in its own right, and it also can be processed to create desulfured fuels and other valuable chemicals. A preferred initiator combination has been identified, comprising at least two different sulfate peroxide compounds. One type or class of initiator can be called a “primary” (or major, main, principle, dominant, or similar terms) initiator, and the other type or class of initiator can be can be regarded as an “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). Various other enhancements to the MSA manufacturing process also are described.