Easiest way to avoid this is to not check your split times. If you realise you are up, you put pressure on yourself. Instead, concentrate on each corner as comes to maximize each one individually then check your time at the end of the lap. It's about the laptime.
I know but it's impossible to avoid that in the game. Even if you had all the split times off there is still one gauge in your steering wheel. I just can't force myself to not look. At that time 56.5 would have been top 5 time so I just froze. It came so suddenly. I had a split time of 56.6 as "Massa's" time and I was below it on both sectors and knew I was able to be a tenth faster than him in the last split.
I always drive split times off if I quali for an event in iRacing for the reason you mentioned.