That would work but it is a complex page to have to maintain a custom version.
There is not a way to add a tab there. One alternative I can think of is to make a custom user profile property configured to use ISettingControl which is just a UserControl that supports a very simple interface. You could hard code values for the get and set interface and not even use the interface. But this would get a custom UserControl on the page in the Profile tab. From the UserControl I would just link to a custom page where the user related data would be displayed. You can easily get the current user and pass his userid or userguid to your custom page as a parameter.
The user profile documentation doesn't cover ISettingControl, but if you look in the comments in the mojoProfile.config file in the root of the site it has some examples using iSettingControlSrc
Hope it helps,