I realized that Challenge Stages don't show IGT So I just took the starting times and subtracted time left when I entered the portal

I'll write the times below Challenge Stages 1 and 2 - 2:30 Challenge Stage 3 - 3:30 Challenge Stage 4 - 2:45 Challenge Stage 5 - 4:00 Challenge Stage 6 - 2:15

Brilliant idea.

Btw, just out of curiosity I would like to know why you feel IGT so important to keep register as RT?

It's just for fun to be honest. The game mostly keeps track so why not?