I think that you have a caching problem on your joomla front end.
That's why the token checks fail. Luckily, the token checks aren't really needed during the checkout so I gave you a modified version of the checkout controller without the token checks.
Now that there is no check, it works just fine.
If it doesn't on your end, all I can think of is that your browsers have the pages cached or that you use a proxy server which cached them. You should try to flush all the cache of your browsers/proxy and try again.
On our end, all the tests are positive so there is no problem anymore I think. It's just that you don't see the changes on some pages because of some cache.