First of all. Get rid of those unsightly screws!!!! Plug the holes with wood putty and then re-urathane. shame on him. I'm sure you have already told him that!
Squeeks are a good thing. You always know when someone is coming
I have an older home and I am keeping mine.
If you are interested in eliminating them the best way is from below the floor at joist level. They can be a headache to fix depending on humidity levels throughout the year.