I would cut the video into small chunks and store them in a Dropbox folder over a wireless connection if I wanted to implement this myself in an area where you could get an affordable unlimited data plan (that is the case in some parts of Europe at least). If that's too much data for you for bandwidth and/or cost reasons you can instead grab individual frames out of the video scream every second or two and save them as a JPEG files to be uploaded to Dropbox.

I use this solution in a non-car surveillance application but, admittedly, there's an x86 Mini-ITX board running Linux involved.

Edit: phrasing.

These are $60-100 units, they are pretty basic protection.

You have a free data upload link from your car?

Using cellular broadband, but only in case of an emergency, would still be useful.