Careful with the Clorox full strength.
I this house I stored a gallon bottle of the stuff under the master bed/bath sink. I didn't realize the bottom was cracked with a slow leak. It turned the plywood floor of the cabinet into jelly, 3/8 inch deep, in a big ring matching the outline of the bottom of the bottle. Of course it was sitting there for weeks before I noticed it, but still...
One of these days I'll fill the gouge with plastic wood, sand it and paint it, and it will be almost as good as new.
As for the blued floor... I think sanding and refinishing might be the best solution. You don't want to add stuff to it that will make it soak in more. I'd call in a professional wood floor installer/finisher and ask for their opinion. No offense, but from the looks of it that floor has gathered a number of deep scratches anyway that refinishing would fix.