You and the customer have both fallen prey to the "100% utilization fallacy." This puts the project at risk. Build more slack into your project management process, not less.
[T]he customer has raised an objection that since she is not technical she will not be able to fill her "slack time" with development time...In reality, we just don't think there will be any slack, and in fact a technical PM is a bit worrisome for us as it is a large project and we want to make sure that the PM takes care of all the team members. Communication with the customer takes 3+ hours a day with all the emails, and meetings by itself.
Both you and the customer are making the same error. 100% utilization of any resource is undesirable. It is a "project smell" that causes bottlenecks, reduces flow, and prevents the project from dealing with even a normal distribution of schedule perturbations.
Expecting more than six hours a day of "real work" is not pragmatic. If your project's communications overhead is already projected at 50% of a project manager's capacity, you're essentially saying you expect that person to actually manage the project in three hours per day or less.
Is 15 hours a week of gathering status, reporting, schedule adjustments, preparing project management artifacts, and other routine tasks adequate? Probably not.
Even if it is, is there sufficient slack in that time allocation to handle unforeseen events, resolve problems, or handle anything that is not strictly routine? Again, this seems unlikely.
You need to build more slack into your resource allocations and scheduling, not less. Anything else is setting the project up for failure.