Points to note.
(a) 12.1 steers the calculation to a discrete obstacle analysis while 12.3.1 provides an acceptable alternative (provided one considers the intention of 12.1)
(b) there may or may not be a first segment. If there is one, then it has to be considered in the obstacle analysis
(c) The B767-200 is only limited, concerning climb requirements.. refers, I suggest, to WAT climb gradients only which are considered independent of obstacle clearance calculations
(d) Systems Used to Find Maximum Take-Off Weight With Obstacles .. can be true IF AND ONLY IF (and I would be very surprised if the particular large Australian carrier to which you refer got something so simple wrong) ..
(i) there is no first segment, and
(ii) the third segment acceleration phase is scheduled at a gross height such that the net third segment height clears all obstacles by 35/50 ft as necessary. This is a major failing by many when using the ERSA RDS data as it is too, too easy just to ignore the third segment and, potentially, run into a bumpy bit, depending on the length of the third segment .. simple geometry at work here
(e) as discussed earlier, the distance deltas which you quote are very specific to the Type and a generalisation, absolutely, is invalid
(f) we could go into a whole raft of different flowcharts dependent on various typical AFM protocols (and there are many varied ways of doing the AFM presentation business) .. suggest you restrict your question to a particular style of AFM presentation and a number of us can give you the story according to how it should be done ...