what i did was use the rubber wrapping of the otterbox as well as the front part of the actual hard case. with the phone and the extended battery with the backplate hyperion supply, its impossible to fit it into a defender case with the whole hard shell, but what i did was plop the phone in the rubber wrapping, (with the hyperion extended battery and back plate it came with) and then just put the front portion of the hard shell on. it takes a bit of force to get the edge wrapped all the way around the front part of the hard shell because of how much more space is occupying the rubber portion, but it actually fits perfectly. i've always thought with the otterbox hard shell there was too much wiggle room between the rubber and the hard shell in the middle of the back of the phone anyway, but this fills it in perfectly.
unfortunately because i'm a new user it won't let me post the link to the battery+case combo, but if you google "galaxy s3 hyperion 4200" its the third link @newegg
the only problem with this setup is that because you have no back portion of the hard shell in place, the pieces of rubber that cover the headphone jack and the charger aren't locked into place by the hard shell anymore, and because the side locks of the hard shell are located on the back portion, you can't put the phone into the belt holster because it has nothing to clip into anymore. in my case, i never use the belt holster, and the headphone jack and charger cover don't flap around or anything, so it works perfectly for me.
the problem i had with the cutting of the hard case solution is that if you were to drop the phone and it landed directly on the battery, theres a good chance somethings going to break. with the backplate that hyperion offers, theres still plenty of heavy duty plastic (and rubber with the otterbox case) between the ground and the inner workings of the phone and i get the insane battery life of the 4200 mAh battery.
unfortunately i don't have a camera to take any pictures with at the moment, but figured i would post it here so hopefully someone else can enjoy the same type of setup i have.