I read your question to my husband and this is his take. It's probably going to be very expensive because you have to make a lot of structural changes that involve moving load bearing walls.

If you don't need your third bedroom, another option might be to place the DR there. You could place the door opposite the kitchen entrance. It could easily be restored to a BR when needed.

What you want is doable but I don't see moving the stairs really giving you much useable space, especially considering the space you'd be using to relocate the stairs. What doesn't work with the current setup?

We are thinking the same thing, we would like to move our stairs to (right side on picture) wall to basement. Which way to do your floor joist run? Fortunately our runs with the planned new stair well. We would lose some living room space but gain much more open concept on both floors. Good luck. :)