I then nominated my heading and told my examiner how long I would need to stay on the heading for, doing a bit of ready reckoning for how much my groundspeed and track would be affected by the wind
The objective of the diversion is not to get there quick, but to get there at all. Your tip on starting the diversion at a well-known landmark is a good one, but there is no requirement to do a dead-reckoning leg after that. You can also feature-crawl if you want to (otherwise known as IFR: I follow roads, railways, rivers, ...) even if that means a longer route.
And if you are already overhead a well-known landmark, there is no shame in orbiting there for a few minutes until you've got it all worked out.
Do keep a good lookout though.