I am sorry to learn about your landlord's rent increase.
While your mathematical calculations are correct, the legal one is not.
The 30 days/60 days notice provisions apply for "periodic tenancies" (week to week or month to month) tenancies. You are receiving a notice at the end of your 12 month tenancy giving you notice that if you wish to remain in the property after the end of your 12 months, you must sign a new lease.
Many tenants take it as a matter of course that they can continue living in the unit after their initial 12 months (or whatever initial term they have) expires - but this is not the case, unless the lease provides for a "month to month" following, they sign a new lease, or the landlord allows them to "hold over" (meaning they stay in the unit but do not have a formal lease - but the landlord doesn't kick them out), they must move when the 12 months is over.
So, your landlord is giving you the option at the end of your 12 months: you can sign a new lease for a period of time (you say they are offering a 2-12 month lease period), or you can go month to month but with a substantial rent increase.
This is not affected by the 30 day rule for periodic tenancies.
If you had a "month to month" tenancy, your calculations/argument would be correct.