Firstly the time variance we're talking about is small and will only matter when milliseconds matter, secondly I addressed this - for scientific measures and scenarios where milliseconds matter a different time unit should be used.
If you want to prioritise ease of moving between the two systems, I'd suggest a normalised version of the new second. If you want to prioritise science, then something that makes a nice round number when giving the speed of light would be nice. If you want to prioritise ease of adoption, just keep the current SI second, just stop using it to measure times of day.
Either way the symbol for writing it should be different.
If you want to prioritise ease of moving between the two systems, I'd suggest a normalised version of the new second. If you want to prioritise science, then something that makes a nice round number when giving the speed of light would be nice. If you want to prioritise ease of adoption, just keep the current SI second, just stop using it to measure times of day.
Either way the symbol for writing it should be different.