Base 10 is not good. 10 just does not have enough factors, so we are left to deal with complex fractions. Let's instead use base-12 numerals and keep time unchanged!
In base 12, 1 year is 10 months (or 265 days), 1 day is 20 hours, 1 hour is 50 minutes and a minute is 50 seconds.
Easy enough!
Edit: wait! I just realized this is still not ambitious enough!!!
What we need is to halve seconds in two. So, in base 12: 1 day = 10 hours, 1 hour = 100 minutes, 1 minute = 100 new seconds.