You can run analog video on active baluns (nvt?) up to a mile.
RG6 is normally rated at max. 1000 feet. It depends on the IRE requirements of the recieving device. There are cases where up to 1500 would be possible, but you may be pushing it for a readable sync. level. Video input level will be reduced.
I would not want to use my time trying to push for a solution regarding hdcvi.
With this being almost half a mile, I would assume this is another building, or a remote pole or site, either probably with a potential ground differential, which will jeapardize the input port. Most HDDVR units come with IP channels, so it is best to try local power to the camera with 5ghz radios back to the recording unit if near line of site is possible. Copper and ground differential is a bad scene and liable for problems, especially during electrical/lightning storms, or if the camera is grounded. Fiber and/or wireless is the best solution to an IP based solution.
If this is a remote building a half a mile away, use a second hdcvi recorder. We get 4 channels with drive for less than 300 bucks. Cheaper than a return trip and a "now what do I do".