How do I get iOS Reminders to recognize my location/geofence better?
The Reminders.app does not allow you to customize the geofence perimeter in the application. In iOS 6, it will allow custom address input versus someone from your address book. 

A way to get around this is use one of the several other apps available. 

I ended up using Checkmark. You can enter custom locations, and for each of those locations, you can adjust the perimeter. This has worked great, I have a larger perimeter around my work, and a medium size one around my house. 

Finally, I think this comes down to the GPS sensitivity in the iPhone 4. My wife's iPhone 4S picks up our location much closer and quicker when it comes to geofencing.