Move the time 1/2 hour, then leave it alone!
How about recognize the clock is based on physical astronomical positioning - and leave it alone!
Just go forward an hour and leave it there. Pick a time, stick with it. It's all relative anyway.
Back when Amelia Earhart was flying around the world, the island she was trying to land on (Howland Island) was on a 1/2 hour shifted clock. The Navy ship a few miles off Howland was using a clock referenced to Hawaii time and was on an hour shift. (Ship time was 1100, island time 1130). I forget what clock Earhart was using.
The ship had higher freq. communications and would attempt to contact Earhart at 15 min. and 45 min. past the hour, while the island had low freq. communications and would try contacts at the hour and half hour.
Earhart had to switch between the frequencies at the proper times, plus trying to use a tracking beacon frequency..
They figure the misscomunication of the time was one of the numerous problems that led to Earhart missing Howland Island. Based on the Earhart investigation everything military and shipping, etc. went over to GMT.
--Move the time 1/2 hour, then leave it alone!--
Each town should be able to set their own time - just like it was done by our founding fathers ...
LOL!