Have you tried assigning a static IPv4 address on your phone? I'm not absolutely certain this will keep it from acquiring an IPv6 address anyway, but it's worth trying.
Beyond that, I'd see if you're having issues loading the same websites on the phone's cellular connection. If not, try disabling IPv6 on your WiFi router and see if the loading issues go away.
Addendum: You may also consider using another DNS server on the phone, such as Google's Public DNS (8.8.8.8, 8.8.4.4).