You don't need "three instances of the phone fields", you just need one portal, with one instance of the phone field inside that portal, and set the portal to display, say, 5 rows. Then, when you add a phone number, a new blank row will be created at the bottom of the portal, ready for you to enter the next phone number.
Also, in your phone table, create a text field and call it "Category". Create a Value List using custom values: "home", "cell", "business", etc. Add the Category field to the portal and then format the field as a drop-down or pop-up menu (and attach the Value List to it) so you can select the category for each phone number.
Thank you! I'm not exactly sure what I was doing wrong before, but that seems to work.
The secret is checking 'allow creation of related' in your relationship dialog. :^)