I'm pretty sure once your tenants have gone month to month (either by your presenting them with a MtM agreement, or their existing agreement stating that it converts to MtM, OR BY YOUR ACCEPTING RENT AFTER A FIXED TERM LEASE ENDS then legally they are MtM you cannot force them to accept a new lease agreement. You can still offer them said agreement but its entirely their decision if they want to accept it or not. That said, you can still offer both the carrot and the stick insofar as offering fewer/less rent increase if they agree to a longer term lease. Just be sure to give enough notice for rent increases. In seattle its now 180 days, not 30 or 60, AND if you increase rent more than 10% and the tenant's income is below a threshold and they move anytime in the next six months you will have to pay relocation assistance. (but oh no its not rent control....)
You can still amend rental agreement terms by issuing appropriate notices of rule changes. Just don't try to replace the entire lease with one notice for rule changes. (So I've been advised by somebody who is an authority on such things)
Editorial: Since laws on this changed in WA to not allow landlords to issue no-fault terminations I've now had two tenants willfully refuse to sign lease renewals forcing me to decide between accepting their rent payments and letting them go MtM or refusing to accept the rent and risking a protracted battle to remove them. In both cases the tenants in question were paying rent as agreed but adversarial - one was a hoarder we (me + PM) constantly had to lean on to keep their behavior within tolerable limits but they were emboldened with "just cause" law changes and when the pandemic hit and we couldn't threaten nonrenewal. That tenant thankfully decided to move on their own after we refused to allow them to start piling stuff in the carport and other common areas; something we could still control; basically we told them we would start discarding any items left outside and they couldn't handle that. The other tenant (inherited - outside seattle) had brought in additional occupants and also had too many dogs (but were allowed by prior owner) for the space and is resentful of our efforts to get roommates onto the lease and to get them to control the dogs and not wreck common spaces and to clean up after their pets and so have lashed out in various ways; one way was refusing to sign renewal, even though it had no rent increase or significant terms changes. With them we eventually gave them ultimatum of all adults sign lease (which had specific provision so they could terminate early ; something they gave as a reason for not wanting to sign) or accept a 10+ percent MtM rent increase. They made a huge fuss and lots of sometimes less than polite noise but ultimately chose to accept the rent increase.
Fun and games but unfortunately also new normal (in WA) I think.