I use mean green degreaser or greased lighting and a non scratch scour sponge and goof off carefully in tough spots with a rag.
Funny, how there is a recent thread with tips on how to get the new w/w John tires to mellow and look aged with wood stains and this thread to accomplish the reverse.
My take is clean the original tires, but embrace the fact they look old and match the bike...as paint, tires change with time and I only use original tires (with the rare rider exception, partly to avoid a broken clavicle, but mainly to not ruin vintage tires!)
I buy whole bikes sometimes just for tires that look like yours.
Chris