Short of wiping my iPad to clear these out, what is the solution?
There is no sure fire way to remove website data other than restoring the device to factory setting.
I wouldn't worry about cookies. Cookies are added/kept to make surfing faster.
That is the way internet works.
Evercookies are never going to be removed until you "wipe" the storage clean.
If you wish to remove a specific cookie, try visiting the site.
While the site is open, remove website data.
Clear History Caches and Website Data. https://support.apple.com/en-us/HT201265
- To clear your history and cookies, tap Settings > Safari > Clear History and Website Data. Clearing your history, cookies, and browsing data from Safari won't change your AutoFill information.
- To clear your cookies and keep your history, tap Settings > Safari > Advanced > Website Data > Remove All Website Data.
If you are worried about third party tracking your search history, use Private browsing.
Note: AutoFill will not work in Private browsing mode.