Overwatered plants simply need to dry out; they don't need the soil replaced. When repotting, it is never a good idea to remove any soil because doing so tears away the tiny root hairs that usually go unnoticed but do most of the work. That causes what is commonly called "transplant shock." It can be avoided if the rootball is left intact. There was nothing wrong with the soil except that it was too wet.
Going forward be aware that your plant is now in recovery mode as it tries to grow new roots. It will continue to lose more of the older leaves. Discolored leaves can be removed because they will never recover.
I suggest that you remove all the soil you added to the top of the original rootball so that the uppermost roots are just barely covered. That will allow oxygen to penetrate the root zone more readily. Then wait until the top inch of remaining soil is dry before adding just enough water so that it dries out similarly again in a week. Experiment a bit to see just what the right amount of water is.
The watering is tricky but critical to getting the roots to recover. It will require much patience on your part because it will take a long time before you see any improvement.
No reason to cut back stems unless they shrivel and get soft.
