A more simple solution is to have 13 months of exactly 28 days, plus one day for new years day. That's even better because every month is exactly the same number of days which means semi-monthly and bi-weekly billing systems are the same thing. And because there's the same number of days anything billed per month can be easily prorated per day, and any billing cycle will match up with every other billing cycle... so basically everything imaginable becomes considerably easier.

The only real problem is coming up with a name for a new 13th month and where to insert it.