Hi, I'm Heather, an attorney with 15 years experience.
If they file the eviction, the judge won't really care that they were stalling. I know - annoying. The judge will look at the lease, and if it provides that the month-to-month rate is $1,950, and that you've not paid it, that's all there is to prove that you are to be evicted. They are under no obligation to renegotiate if they do not want to, even if they are leading you on. The plain language of the contract is what will control.
It sounds to me like they have no intention of renegotiating your rent, and that they want the $1,950. If they were interested in renegotiating, they would do it, because they know that you've been asking about it for a while.
If they file the eviction, in most jurisdictions, you still have a bit of time - usually at least a week or two, from when they file, to when a sheriff removes you. Moreover, if you respond to the eviction (rather than doing nothing), and demand a hearing, even though you might lose the hearing, you will have more time before the process can be completed. I have seen evictions take 30 days or more. Just be sure that you read what is delivered, because you don't technically have to be out until the sheriff comes and escorts you out.