I was taught a couple of quick tips for the diversion leg;
Firstly, you dont have to start the diversion immediately. When I was asked to divert to X, I nominated to start the diversion route from the big town I could see a couple of minutes straight in front of me on my current heading. That gave me a couple of minutes to plan the diversion heading and draw it on the map before I turned onto the heading and started flying it;
And, as an alternative to the "standard thumb", I had drawn out a scale on the back of my PA38 checklist showing minutes of flying time at 90kts, and measured it against the line on my map.
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
good luck