This really bugs me. We run a lot of sheep, on pretty remote and steep ground, and make every effort to bring everything dead back in if at all possible and have it collected properly, paying the fee each time, so I don't see why other people can't too.
Re the record keeping, as you do sometimes get either something in a ravine or similar that you either can't get to without endangering yourself or don't find for ages, or we also getting badgers chewing off ears complete with tags, I run two separate lists, an unkown deaths list, which records anything spotted dead somewhere where it is not safe it get to, or with the tags gone, and an 'AWOL' list, which is a list of tag numbers of sheep which have not appeared when I would expect them to, i.e. have not come in to be divided in to groups for tupping, have not come into the shed for lambing etc. These two lists are then cross referenced after the sheep has had another chance or two to reappear, and recorded in the flock register as 'black loss' which is perfectly acceptable to inspectors as long as the numbers you are recording in this way seem reasonable for your situation.