@Jason Hines I'll defer on the eviction question to someone that may be able to better answer. My gut says that if they don't move out (whether because they can't or don't want to) then you'll have to go through the process.
To the other point, I would be more likely to have a casual conversation and just explain to them.. look, market rent is near 1200. If you would be open to signing a 2 year lease, I would hold your rent at 1000. They've been there for 10 years, and I'm sure they are probably nervous about a new landlord coming in. I would make it seem as though you weren't going to change a whole lot. The longer the lease they sign, the lower the rent I would consider.
Remember that if you get that 1200, versus 1000 per month, that's 2400 extra per year. 2 months of no rental income is 2400 at market rent (I usually assume a turnover is 3 months including time to get the tenant out, reno, and time to find a new tenant). Granted ($2,400 x years stayed) can add up quickly.