How do I create a home screen button with a tel:// URI?
As it turns out it is possible to create a profile in Apple Configurator that creates the button(s) you want, save it, and then send it to the person to install, which will then add the buttons. Totally painless on their end, so I can certainly deal with creating the profiles. Hope this helps someone else.

Short summary:


Get Apple Configurator form the Mac App Store
Turn on supervision and create a new profile on the general screen


Go to Web Clips
Add a new clip with a url in the form tel:+12025551212
Add more clips for more phone numbers

Save and export the profile and mail it to the user