Found this discussion searching for other ideas regarding battery power for a Mini. So who's battery pack is your system wearing? Also would this Wiznet system work, http://www.shopwiznet.com/wiz820io I was given one of them at the first Maker Faire that I attended that I bought a weekender for.
The two salesmen were at the Parallax(!) booth, but I surmise that the little devil would work with anything that supports properly delivered SPI communications.
So the question is, would that fellow work in place of the module your using?
The battery I was using is a Ni-MH 6-cell battery pack delivering 7.2V under 1300 mAh.
Regarding your W5200 module: I don't know if this will work but is worth giving a try as you have it anyhow and won't hurt anything; a quick superficial comparison of the two datasheets (the one of the W5100 and W5200 chips) shows the same register arrangements, but this alone doesn't mean that they have kept backward compatibility. So how about trying it out, and maybe upgrade the driver if required, and send it back to Secret Labs?