Unique problem you have here but not impossible.
I would go with solar panels on the top of it (if you don't think they will be vandalized) to a battery in an enclosure in the container. I would go with a wireless camera so that you can connect directly to a Wifi hotspot (Verizon and several cell providers offer this for a monthly fee). The hotspot can just be permanently charged and stay on all the time. However, with the data rates charges and limits this might prove expensive.
Any reason you can't just go with local storage?
We could use local storage but, because there might be periods of weeks when we don't visit the site, it would be useful to be able to check it remotely.