I'm trying to quiet a squeaking floor in our kitchen. It has recently started to get loud. When I looked at the floor from the basement, I saw someone had driven in dozens (several dozen, really) staples through the floor. They were in a rough, random line along a distance of 4 feet along this piece of plywood subfloor, but strictly between the joists. The staples were protruding a half inch from the wood, and they had strongly splintered the bottom face of the plywood. I think this had weakened the subfloor, so that after many years of walking on top, it has started to stress the subfloor. Above this is directly in front of the kitchen sink, as well as the stove, so it is a daily high traffic area. However, there is no sign of water damage that I can see. What you see in the picture is after I've gone through and cut the protruding staples off with an oscillating saw, so much of the splintering is gone too. It looked way worse at first.

Why they had to use so many staples in a small area is hard to guess. The flooring above is a no-wax vinyl flooring. It is 30+ years old now, but we really do not want to replace it, and it is still viable.

My thoughts are to first laminate a piece of plywood to the floor from below. (How thick? Do I need 3/4" ply? Is 3/8" sufficient or inadequate? I have some 3/8 in stock, if that would suffice, but I want to do it right.) Do I use liquid nails to hold it in place? Polyurethane glue? Finally, to truly stiffen the floor, and to hold the plywood in place, I was thinking or running a few 2x4 pieces across, between the joists, and screwed to those joists, with glue also to attach the 2/4s to the plywood stiffener. That would stiffen the floor, as well as hold the plywood in place while the glue dries. How long do I need to wait before we can walk on the floor while the glue dries?

Do I need to go in with an angle grinder over the entire area to make sure I have ground off all the protruding staples? I don't want to take a risk and find that anything I do then pushes staples back up through the vinyl flooring above.

The bays between joists on either side of this one had few or no staples, but they do also squeak somewhat. I'm thinking the subfloor in this one bay has gotten so weak, that the entire floor can now flex a little on either side. So I probably need to stiffen the floor on either side too.

I'm thinking my plan might be overkill, but not actively bad.