Question: How Do I Mask My Web Browsing Activity Behind a Victim Machine's IP Address?

I'm running some stuff on a machine on which I have a persistent Meterpreter session. It's a Windows 7 machine. I can elevate to NT/System, but I don't have access to the router admin page.

Anyway - I want to mask some of our overlapping web activity. It's not enough to disguise my external IP address -- I need to somehow mask it with the victim's external IP address. It's a workplace domain, so they're using a static IP from a wireless connection.

I'm assuming this will involve some sort of tunneling/internal port forwarding, but I haven't been able to figure it out. My IP still shows as my C2 server.

Any help would be very appreciated.