Hi Steve -
I can't answer your question about launching from South Dakota, but I can certainly help with your other questions.
As far as I know there is no payload insurance, but your homeowner's insurance MAY cover the costs if you lose your payload. While the go-to cameras that most people use are GoPros, there are far less expensive cameras that work just as well. For example this camera rivals a GoPro, and is currently only $70. https://www.amazon.com/YI-88001-Action-High-Resolution-Bluetooth/dp/B016MAUHOK
Most definitely use two, completely redundant GPS systems. At some point one WILL fail, and if it is your only one, you lose your payload. My son and I use both Trackuino and Fona systems, both of which are independently powered. Having the two has saved our payload a number of times.
The easiest way to improve battery time is to replace the battery with a 3D printed dummy battery which has leads out of it to a larger battery. My son modelled the batteries for all of our cameras using Solidworks, and our local library printed them out. We then run the leads out to Adafruit 2500 mAH batteries, which are multiple times more long-lasting than the built-in batteries for the cameras we have. Pack these batteries in close proximity to the other electronics to prevent them from getting cold.
We have not found hand-warmers to be especially useful. The cheap ones you get at Walmart only work in an oxygen-rich atmosphere (they essentially burn iron to iron oxide), and thus die out near apogee - they also have the unfortunate effect of releasing moisture as they work. This will condense on the electronics inside your payload as the temperature drops and can short things out - learn from our mistakes. The solution we have come up with is to pack all of the electronics together as much as possible and make sure that the payload is sealed off from the outside. Our payload boxes are all styrofoam which is a very good insulator and can keep the inside of the payload from dropping to the extreme temperatures seen outside the box. The radio transmitter that we use pumps out a decent amount of heat, as do the rest of the electronics.
Please do ask any and all questions - this is a fascinating hobby to have, but is full of a bazillion details and pitfalls that have to be worked around.
Best of luck!