With the appropriate tools I can discover where an email came from, could Voyager trace messages (I'm aware they don't use e-mail), determine its origin, and essentially plot a course home?
I think you've misunderstood slightly. Despite the crew's repeated statements to the contrary, the USS Voyager isn't lost, they're simply very far from home. Within seconds of arriving in the Delta Quadrant (in the pilot episode) Ensign Kim uses the sensor array to accurately locate their position and identify a suitable route back to Earth.
KIM: Captain, if these sensors are working, we're over seventy thousand light years from where we were. We're on the other side of the galaxy.
The Hirogen Network
When they encounter the communications array in VOY: Message in a Bottle, their first thought is to send an audio signal. It degrades quickly (for, erm, reasons) and the network bounces it back to them. Their next idea is to send a self-correcting holographic program along the network, which ends up working in both directions.
The fact that they're only sending signals would suggest that the required bandwidth to send a person (via transport) simply isn't there or that the risk of their signal degrading en-route is simply too high or that the technology simply wouldn't support it.