My ISP has apparently made no progress whatsoever with IPv6, but I've got an IPv6 enabled VPS.

SSH makes it trivial to use that VPS as a SOCKS5 proxy. Just do:

ssh -D 8080 myvps.example.com

Then set your browser's SOCKS proxy to localhost:8080. In Firefox on Linux, this is Edit > Preferences > Advanced > Network tab > (Connection) Settings > Manual Proxy Configuration. Leave all fields blank except for SOCKS Host and Port -- localhost and 8080, respectively. Choose SOCKS5. Then browse to about:config and change change network.proxy.socks_remote_dns to true. This tells Firefox to ask the proxy to resolve names instead of trying to resolve them using your ISP. Chrome worked for me without hassle.

Go to test-ipv6.com to test that it works. If your results from test-ipv6.com indicate that IPv6 name lookups are failing, make sure you've got that about:config setting mentioned above changed.