Increasing rent on a significantly underpriced rental

[Josh B. James]

We have a rental that is currently under a month-to-month lease. The current tenant has been paying $825/ mo, on time, for the past 3 years, but market research suggests we should be charging $1600 - $1700/ mo. The tenants are capable of renting at that price range but are obviously accustomed to the $825 rate they have had for the past 3 years. 

I've read up on offering 3 rent tiers in a rent increase notice, which I would like to incorporate, but how much should I raise rent and what should the timeline be to get the rent up to market rates? I'd like to get it to market rates as quickly as possible without spooking the current tenants. I image a 3-year timeline:

Yr 1 - $1,000/ mo (1 year lease), or $1,100/ mo (6mo lease) and $1,200 (month to month). 

Yr 2 - $1,200/ mo (1 year lease), or $1,300/ mo (6mo lease) and $1,400 (month to month).

Yr 3 - $1,400/ mo (1 year lease), or $1,500/ mo (6mo lease) and $1,600 (month to month).

Has anyone else dealt with this, or have any strategies to reduce sticker-shock/ timeline to reach the market rate?