Let's try to phase it in gradually. We'll petition congress to move to base 12, but will compromise, and use base 11 for a while. Then, if people are still not ready for base 12, we can move on to base 11.1 for a few years, then 11.2, and so forth. Maybe once we get to 11.5, we can start a sliding scale where the base increases slightly every day, so people aren't inconvenienced.

The first gradual phase should be to give everyone two extra fingers: https://www.youtube.com/watch?v=DRjmRNsPl1M

We could use genetic engineering so people have six fingers. However better would be to genetically engineer humans to have four arms and ditch the pinky, then we could use base 16.

Cultures that counted in base 12 used each finger segment (there are 12 on a hand), and used their thumb as a pointer. So we already have all the biological tools needed.

Or perhaps engineer another set of knuckles to bring the count from 12 to 16

Base 12 is better than base 8 or base 16 as it divisible by 2, 3, 4 and 6. Having halves, quarters and thirds is nice.

Base 12 is better than base 16 because then you have halves, thirds and quarters.