I have read elsewhere here that if I ring to re-route after the outgoing sector has been flown that it's possible that I can re-route with minimal change fees as they won't re-price the ticket then.
You can do this but be aware that the appropriate fare classes on your desired flights may be full by that time. For instance you may find on your desired flight the availability is J9 C7 D0 R0 I0. If you had purchased an I- fare, you could not use it on that flight. So you would have to pay the difference to upgrade to a C-class fare (at the historical price) and pay the appropriate change fee on top of the price difference.
So it can be a bit of a gamble unless you know it's a route where there are plenty of options.