Just a footnote about the tournament that gave rise to this - the teacher who raised the issue has since emailed me, thanking me for my efforts in running the tournament, and admitting that there are no easy solutions to the tie break problem - so all is well on the diplomatic front!
I have to admit I am partly to blame for getting into this situation in the first place. I encouraged the player concerned to enter, even if Morrisons refused to give him time off (he didn't know until the day), thinking he could play 3 rounds, and this would be valuable experience for him. He is a new player, who has appeared "out of nowhere", and has suddenly started beating everyone in sight (including me). We were actually running a little ahead of schedule, so he was able to play in Round 4, and the rest is history.
With hindsight, I should have anticipated the possibility of a tie break problem, and announced in advance precisely what the rules would be. I haven't done the maths, but with 23 players, a 5 round tournament must be very likely to require a tie break.
Jack's point about TPR is borne out by the results of this tournament. "Player D" had a TPR of 145 from 4 rounds, his three rivals, 131,136 and 129 from 5 rounds.