I'd like for every week to be 5 minutes shorter from January to June (so that morning hours progressively move earlier approximately as the sun rises), and then

I'd like for every week to be 5 minutes shorter from January to June (so that morning hours progressively move earlier approximately as the sun rises), and then the other half of the year 5 minutes longer. Just adjust the clocks every Saturday. Of course, this should have been implemented 100 years ago, now it is very unlikely when even leap seconds are a problem.