Some thoughts about the soiled hardwood flooring:
1. I'm not sure I'd be too worried about maintaining the "look" of the hardwood floor at this stage--as you'll be carpeting anyway. Good quality carpeting realistically puts off any future flooring decision (say, re-finishing the hardwood) for perhaps 10 years. (I think the average person is in a house, what, about 7 years?)
2. What's more, the stained portion of hardwood flooring may have to be replaced anyway when/if you refinish down-the-line. (Again, perhaps 10 years off!)
Obviously it depends on your situation, but given the above, I'd be tempted just to cut out the soiled section, replace with a strong and properly-installed plywood "patch", carpet and enjoy!...and worry about fixing the hardwood down-the-road when/if you deal with it then. The hardwood will probably need other TLC then anyway.
I should mention that I don't say "just cut the hardwood" lightly--as I'm currently looking at a lot of work on fixing up an old (20 yr) oak floor myself...
Again, good luck!