Well, you could change the nature of the internet and require every single email user to use the exact same email client.
To illustrate the differences between clients, set up email accounts with outlook.com, yahoo.com, gmail.com, aol.com, and any others you think might be useful.
Then, send yourself an email to each one with the signature you created. Take screenshots from each email provider, and show them to your client.
That should help illustrate that there is a host of differences between each email client without too much extra work.