If I were you I would simply continue with your plan A, and move out at the end of April. Particularly since the landlord is not responding.
Of course, I prefer to avoid situations that might turn ugly in general and limiting any potential liabilities, but that’s just me.

Is it true that you have no signed lease agreement at all, only verbal ?
It also appears that the owner is rent-skimming (charging rent and not paying the mortgage). Did they also finance as owner-occupied ?

I would not be comfortable without a written rental agreement (ever, actually), but especially in this case. Do you have any other relationship (friend, relative co-worker, colleague) with the landlord that makes you trust their word ?

Also, if the rental agreement is verbal …
What about security deposits ? What about check-out lists when you move out (in case the place is ransacked after you leave) ?