Are you able to configure the netgear yourself, and forget the slingconnection software.

This is the way I have done it all along.
with the netgear, it should be easy to setup an IP ASSIGNMENT for the slingbox. Just go into active connection, and then down on the left to ADDRESS RESERVERATION. and reserve an ip for the slingbox. Make it something within the IP range that you are enbabling with the DHCP.

Then, go to port forwarding, and set the port you want, 5001 is a good place to start, to forward to the ADDRESS RESERVED for the slingbox.

now, got to the slingbox configuration software, and when you get to the part for configure remote access, click on manual, or i'll do it myself. Then, put in the IP ADDRESS RESERVED, and the port you have selected and see if that works.

you will now essentially have a static port for the slingbox, port forwarding for that traffic and remote access should work. If THAT doesn't work, then I would have to say that something is rotten in denmark.