If it were me - I would put the stairs back in. Put the laundry in the basement. You wont get vibration due to concrete floor, you will have a nicer house, better resale and a better investment of time and money.
Well that is a very subjective statement. Our basement is more of a crawlspace hence why the previous owner did this to begin with. The basement is not the type to ever be used for anything other than storage space for a hot water and oil tank.
Thinking about the design of the basement and the walls down there along with where the stairs used to be - those stairs had to have been pretty steep.
I see what you area saying though about the shaking and thats something to worry about with just a regular washer and dryer. I guess the previous owner has had this set up for some time and, based on the size of the house, we have no intentions on moving the washer and dryer elsewhere.
So based on what you are suggesting, we would need to really re-enforce the flooring that was put there. I was thinking about 2 or 4 beams that we could slide in there.