Hi, Tim. I respect your opinion but my daughter just did it my way and it worked for her. The secret is the shellac, 3# cut diluted about one part of shellac to three parts of denatured alcohol. Lightly scuff sand about a half hour after that and go ahead with staining and finishing. She put the shellac on with a roller. This kind of fills the wood and gives the stain a more uniform surface to cover.
I put a spit coat of shellac (5 parts alcohol to 1 part shellac) on about everything I finish but with a pet stain and the possibility of the smell reappearing, I think you should go a little heavier. This is particularly effective on pine floors but it works on oak, too. Try it sometime, Tim.