This is way out...hope it's not too overwhelming an idea:
The fourth 'shed-cam' could be powered, as Brian eluded to, by a battery system with a large enough battery to last
a few days. Charging it is another issue. However, if your three cameras are set up to send their video/audio on
channel A, you could set the shed-cam to channel D, for example, and have an X10 sender/receiver pair just inside
the home pick up the signal on channel D and send it back out on channel A to get that video to your primary receiver.
You'd need to have the sender/receiver pair powered by an X10 controllable module such as an AM466.
You would then create a macro to shutdown the three house-cams and turn on the AM466 so it would repeat the
incoming audio/video stream to channel A.
Yes, the shed-cam would be sending audio/video continuously but being outside and 30' away from the primary
receiver, it likely would not override the three house cams. If it does, the shed-cam's antenna could be shifted away from
the primary receiver to minimize potiential interference when any of the other three are transmitting.
I hate to use the word scam having been recently spanked
but that's kinda what this solution is.
This is the 50,000' view.