Didn't even think about mentioning the stairs earlier - those were mudded originally in the same way as the floor and we tore those out as well last weekend. We figured that if they had lasted 30 years in great shape like the floor that we'd just do those the same way again as well. Only time can tell at this point, 'cause they're in now!
If the stairs were built in a manner that they have survived for that long previously then you should be okay. Stairs however can be a particular problem and don't always survive the abuse of everyday use.