In Los Angeles, you can evict a tenant with a rental agreement for failing to sign a new agreement that is similar to the old agreement.
Does this let you force a tenant on MTM into a 1-year lease? Yes.
However, I do not believe you are within your rights to threaten eviction because the tenant will not sign a lease that imposes new obligations or restrictions on the tenant, such as late fees, curfews, non-smoking (when the tenant was allowed to smoke before), etc.
I think if you proposed that a tenant sign a lease like this or leave, and they went to the housing department it would be viewed as coercion or an illegal eviction.
@Francis A. - Have you had experiences that indicate otherwise?
One other factor, in the landlord's favor, but in my opinion not ethical to take advantage of, is that many tenants are unaware of their rights. I know a number of deals where the new owner just showed up, told the tenants they had to leave and paid them out $1000 each and they went. They didn't know any better. Of course, they could always come back with an attorney or a nonprofit organization and make trouble for the landlord.
To me, in most cases, paying the statutory relocation fee is a bargain when you multiply the additional rent by your cap rate or GRM and see the difference that market rents will make to the worth of the building. I'm generally willing to pay statutory relocation fees to all my legacy tenants in a heartbeat.