The full question
How do you help your clients to see the benefit of design principles when they are heavily driven by delivery timelines?
My two cents
It depends how you define design principles. If you say design principles are simple tips and ideas that you can implement easily to improve the customer experience (like the ones from this series), then it's pretty easy. As such principles are low hanging fruits that you can implement pretty easily.
If you speak of design principles as general guidelines to follow we can steal a few things from the world of branding. Instead of selling design principles I would ask:
Why did you create brand colors, a logo and selected a specific typeface to use for your communication?
Then see what people answer. I assume they answer things like this:
It helps us stay coherent
It drives cost down as we don't have to reinvent the wheel
People recognize us more easily
These are exactly the same reasons why a set of design principles can help, especially when you are under difficult timelines. Because a good set of design principles helps you then take shortcuts when there is no time. You just have to follow the guidelines.
Sure, there is a one time investment to make to decide which of the "design principles" are the ones that fit the organization, but once that's done life gets easier.