Methanol is found in some car de-icers, and can be dry-distilled from wood shavings, dichloromethane is found in nitro-moors paint remover, and some others, in an azeotrope with methanol, perhaps you could form a tertiary azeotrope with toluene or xylene, then add water to form a layer, it should form a layer of MeOH with the methanol saving the DCM, cool it first, as DCM is very volatile.
You could most likely save the methanol, by salting out the MeOH and collecting anhydrous methanol.
DO NOT use an organic solvent though, do you not remember what happens with peroxymonosulfuric acid and organics? most likely, if you use organic compounds anywhere in a reaction with H2SO5, you will WISH you had made acetone peroxide.
Caro's acid has been known to cause detonations in contact with organics, mixing with a few liters of organic solvent sounds like you might as well be preparing that other experiment with the 30l of NCl3 right away