We did use GMT before, but then we had a problem a la what you descrive above. I think the clue is that one can easily make a mistake regardless of how you name the time. The best remedy for this is every single drivers approach to the timing problem.
Using UK-time makes it almost 100% certain that I do not make a mistake in the first place, and that is important for me. The race ALWAYS start 8pm UK-time, and if GMT at times change relative to UK time, then the race time in GMT will be variable -> possible for me to make mistake.
So how can every single driver be sure that they know when the race starts when they live far away from the uk?
You can google:
what is the time in London now and then count on your fingers to find out when the race starts local time.
Also, when there is closing up to daylight saving (or the end of it) somebody usually mentions this in the forum and we help each other out.
So to sum up, the timing of the race is a challenge whatever we do. There are two things that can go wrong, I can make a mistake and the driver can make a mistake. Using UK time will ensure that the race will always start at the same time, and it is also easier for me to use this time.
As for the Race Director winning the championship I think I can say with confidence that it will never happen at Presto GP