Do you have the type of wood conditioner that is specifically designed to prevent blotchiness? And how dark were you planning on staining the floors...the same as the trim?

I to would be nervous about the blotching. Might be a good idea to do a single stair tread as a test if stairs look same as the landing. In similar situations I've had pretty good results with colored Watco and other oils topped with oil base varnish or Polyurethane. Whatever you use,stay with one brand/system start to finish.