The answer likely is in the documents that you signed. If the last document you signed incorporated the terms of the original lease (that calls for a 60-day notice), then you need a 60-day notice.
Your agreements likely also have provisions as to how notice for a rent increase must be served. With proper notice, your landlord can set the rent for what he wants unless your agreement has provisions for a limit on rent.
In the commercial rental agreement that I have reviewed, there usually is a provision that once a lease has expired and not renewed, the monthly rent is some percentage (like 150%) above the last monthly rent of the lease.
You can review your specific facts with your attorney.
I concur with Mr. Nguyen. The lease you signed has expired but the terms still apply. I'd have to read the lease to determine whether your landlord's decision to jack the rent for the last month is enforceable or not. He may - or may not - be able to charge you additional rent because you are leaving. Commercial leases are strictly contract, there are no statutory safeguards as there are in residential tenancies.
Luckily, the commercial landscape is wide open and when you go to move, you are going to have good opportunities and it won't cost you so much. It is a renter's market out there.
Hope this helps. Elizabeth Powell