From the image you linked to it looks like you found one of the documents I have been learning from. 🙂
I haven’t played much with the nat tables so I don’t have personal experience with the REDIRECT target. I did find this however: http://www.linuxtopia.org/Linux_Firewall_iptables/x4508.html and it says
The REDIRECT target is used to redirect packets and streams to the machine itself.
So it would seem that filter target is not doing what you want. I am guessing, and I emphasize the word guessing, that you would need to NAT those packets to get them to your desired destination and also to have the returned packets get back to your original LAN client machine. Not sure if masquerade or SNAT is needed. (Like I wrote, I haven’t done much with NAT other than follow a couple of cookbooks.)
And I don’t see how using alternative ports actually fixes your problem.