I’m surprised this isn’t one of the strange features buried in something like a Canon 7D or something like that. Maybe a request to Magic Lantern for something like this? If your not sure what Magic Lantern is look it up…I could give you suggestions of cameras that do this but like you said they would be over $2,000 and usually more than that from what I’ve seen…also I believe Sandisk make one time use SD and CF cards for this purpose I believe for certain legal work using the write once read only SD cards its enough with the EXIF data but I wouldn’t do that without checking with your Office/Department, I’ve seen the Write once SD/CF cards in use with Law Enforcement Officers on standard Canon and Nikon DSLR’s. Best solution would be for in camera burning of the timecode and not just over HDMI if you really need it to hold up to possible questioning of how it was obtained. I’ll see if I can ask some of the officers I know about this subject. Sorry I can’t be more useful but i thought I would post anyways however….