Soap and water are fine. You could even submerge your chain in the sink if you wanted to. As long asy you dry it well and lube it after.

Your problem is the lube itself. The wax is pushed away from friction points (like all lubes) but never returns, because it's wax, not liquid. You ever notice the wax build up is always .25 mm away from where things make contact and rub? Worthless. My 2 cents.

BTW, your previous drive train cleaning procedure was excellent. Don't abandon it.