I would NOT recommend changing the 2 months off; you'll annoy your most loyal customers.
>2 months off for paying annual pricing is a very good deal for someone who plans to use you product on the long term.
I too pay for some things on an annual basis (e.g. email). I guess never expected my product to be sticky enough for people to want to go annual straightaway. To be very blunt because I'm anonymous, how do I monetize this stickiness to extract maximum value from future customers?
Don't. Focus on acquiring more customers instead.
Worked for PayPal, Uber, AirBnB, etc..
Addons/extras/upsells. Find some features that might make the most sense as something that exists outside of your current pricing structure, maybe due to specific fixed costs of some sort that don't make sense to roll into the plan pricing, and offer them a la carte at like $20/mo or something. This would allow you to bump your ARPU a bit.
Another option is services. Not knowing your product, its hard to make any concrete suggestion here, but data migrations and initial account setups are common ones.
Customers will notice a "large" bill every three months. It's just infrequent enough that they don't remember what it was from 3 months ago. It's just large enough that they really want to check where the hell is all that money going to. Customers will investigate and that can only result in cancellation.
A monthly subscription is designed to be easily approved by a middle manager (and fly under the radar). A yearly subscription is designed for customers who plan ahead or cannot do recurring payments (recurring invoices/approvals is a huge pain to deal with).
So I would create a new subscriber role and simply let your new customers pay a bit more.
It is wise to be upfront with existing customers : say you have need for more funds or more investments, relay that to your existing customers, say you are keeping their price (indefinitely if possible) and that new customers going to go into the new tier.
Kevin Hale - Startup Pricing 101