Do they want to change the template dropdown selections? This would require me to rebuild and test all of their templates, and it will significantly limit what design options they have available.

I vehemently advise against doing this and am confident this will lead to a less satisfied customer who has to pay more for less flexibility in how they build their site, won't be able to launch on schedule (not to mention, I won't have any time to work on responsive design), and they will have significantly more support issues.

We've established a nice compromise here. For example, the Sidebar template has been renamed Sidebar (A, B, D, G).