If you have problem with Unix time you are probably using it wrong. It is monotonically rising timer that increments every second. That's it. It doesn't care about leap second, leap years or any of the orbits.
If you think you have no problems with unix time, it's because you never noticed them.
TAI is what you want.
Wrong. It's continuous, it's just not monotonically increasing.
https://www.wired.com/2012/07/leap-second-glitch-explained/ https://developers.google.com/time/smear