Or just use GMT and adjust scheduling local things based on local daylight. Phrases like working 9-5 wouldn’t make sense for most anymore, but who cares. Having the date change in the middle of the day might be odd, but people working night shifts deal with that already.
I think we need to match solar time approximately. The words 'today' and 'tomorrow' and 'noon', for example, have both clock and solar meanings that need to be roughly aligned.
