I was also able to run longer distances when I shifted my mindset to focussing on running the current km (or mile). It’s similar to your ‘just one more’ approach, except that I’m usually following a training plan so set out with the intention to run a pre-determined distance.
Last year I smashed my marathon PB by not once allowing myself to think about the total distance ahead but only thinking about the next mile marker.
This worked a dream and I took 41 mins off by previous best time using this strategy.
Plus I smiled like a Cheshire Cat for the final 5km. Eluid Kipchoge is right about that trick!
Keep up the great writing!