I'm having problems with that page. It crashed Firefox twice and Chrome loaded the page but refused to show the double parity pic. Can you post a pic here please?
So, you're having a problem with corners and parity? What method are you using? Most parity algs are based on you using the reduction method. That's where you solve the centres first, then pair the edges, then solve like a 3x3, fixing parity usually at the second cross part (last layer) but some people save it for the very end.
You might find if you are using this method, and solving parity last that corners become more of an issue. Can I suggest that the single edge flip alg is used when you have 1 or 3 edges of the cross solved, but can't make an even number, instead of ignoring the issue until the end.
If you are using another method entirely, such as the cage, where you solve the centres last, parity might be entirely different. I can't help here since I use reduction method. It would be helpful to know what method you use and exactly what you normally do to solve the last layer.
Please take off topic discussion off this forum. Thanks.