You convince them in the same way you convince a PM to give you time to write tests for your work: you don't give them an alternative. "You want this done? That'll be 20 billable hours." And your estimate includes the time needed to do work you're willing to sign your name to. When I hire a plumber or an architect, I tell them what needs doing, but I expect and trust that they'll put in the work (and bill me accordingly) to ensure that it gets done properly, even though I don't understand all of the specifics of what doing those jobs properly entails.
