Bleach White, Scotch pad (for scrubbing pots & pans), garden hose, & elbow grease! A set of DP brake pads made for white walls doesn't hurt either. HTH!
When I bought my sons bike the back tire was in horrible shape. Westleys wouldn't cut it all off. Even with the Scotch pad. Really surprised me cause I've always used it with great results. Ended up using the Simple Green concentrate with the Scotch Brite pad and had it back lookin brand new again. Still mostly use Westleys but for those stubborn spots I break out the green bottle.
I've used Simple Green before as well, but worry about long term use effecting the wheel bearings. Works great on stubborn stains though if you're careful.
I had the wide white walls for years. I finally just gave up on trying to keep them clean, and went to black walls. More riding time, less leaning time, more smiles per miles. Enjoy them, as I'm sure your time will come when the lights go on, and you realize you'd rather ride than clean white walls. Especially that rear tire. What a pain. Good luck with whatever you use, because I've used them all. It require elbow grease, most of all. Although for my money, Westley's was the best!