You've answered it yourself
> what is the best path to end this ridiculous custom?
> minimum wage
> what is the best path to end this ridiculous custom?
> minimum wage
But I'm not defending the argument, just adding to the debate. I'm fine with tipping, personally, because I think it aligns incentives to encourage good service. That good looking people get better tips doesn't bother me in the slightest—life isn't fair.
2. Greedy enployers can't use the promise of tipping as an excuse so they start to paying minimun wage.
3. Government intervenes making sure minimum wage is paid.
It starts with (1).
Starting your movement with "don't tip" is a great way to punish workers without much chance of being successful. It should probably start with the restaurants, or even regulation.