Jeff,
if a club feels the need to define the edge of the putting surface with a dotted white line then that is up to them. In the absence of such definition it is up to the players to decide what is and is not 'putting green'. I am afraid that you are pushing a point of view just for the sake of argument and it falls down flat when looked at through how the rules are applied.
Sean,
again, a very interesting piece with much to merit it BUT as far as the pros are concerned the problem is entirely down to the fact that what should be unacceptable pace of play has been tolerated for far too long. The pro tour need a jolly good kick up the arse and a 3.5 hour time limit imposed up on them and strictly enforced.
As for the problems with definition at Burnham the answer is to do that which golfers have done for generations when facing such situation. Of course if this proves to be impossible then I suppose the club will need to start painting silly little lines or maybe cancel competitive play