I have a similar situation in the file I'm trying to repair. I am not happy with my skill level but I'm getting closer.
The way I approached the problem was to isolate the area I wanted to affect into a discrete object and then operate on that object. I did it by placing the position cursor at the start of the target and splitting the current object (T), then positioning the cursor at the end of the target region and again splitting the object. This results in a three objects: the one you want to edit and the ones preceeding and following.
Then you can select that specific object and apply normalization (offline effects>amplitude normalize). If you prefer to apply a unique setting to each channel, you can isolate either the left or right channel by enabling the controls at the very bottom of the offline effects menu and then apply the operation to each.
Yes, the key is turning the section of audio into a separate object. That's what I would do. Then you have total control over what happens to that segment. (You won't be altering the original file, but an object that represents it. Your changes won't be rendered until you bounce. So things are very easy to undo.)
Double click on the object and it gives you the object editor. The settings here are not global; they are for this object only. You can choose to mute left/right, or grab the volume slider and set the volume level to zero. Or you could apply fades. Fades can be applied by going back to the object itself. On the object you will see a horizontal line with three transparent squares, one on the left, one in the middle, and one on the right. The one in the middle is for the object volume. This acts like normalize. Drag it up or down to set the objects volume. This is also the same control as the slider in the object editor. The square on the left is for fade in. Drag it to the right to apply a fade-in. The square on the right is for fade-out. Drag it to the left.
Another option is to delete the object entirely. Select the object by pressing clicking on the lower part of the object with the mouse. Then select the delete key. Objects to the right can be moved over to the left now if you choose to do so. If you have set "snap" on, the object will snap into position as you move it to the left. (Snap is the icon on the toolbar with the magnet). Objects will snap to the cursor, or to the object as you move an object from right to left.