After working diligently on stripping the bottom you eventually come to a time when there is just one strip left. If you are using cove and bead strips you will want to have removed the cove from the second-to-last strips so you have a nice straight-sided hole to drop the last strip into. I use the hole as a template and trace the shape of the hole from underneath. I then cut off the majority of the scrap wood being sure to leave enough excess to work on as I refine the shape.
Working on the pointy end of one end at a time I refine the taper to get a tight fit in the hole. As you get the end to fit start working back along the length of the strip. Start out over long because as you refine the shape you will likely end up making the strip shorter.
As you get close to the middle, stop and go work on the other end, again starting at the point and slowly working towards the middle.
By pressing the strip down into the hole where it fits and allowing it to rise up as it gets tight you can then take a pencil and mark the edge you are planing. This mark will travel diagonally across the width of the strip edge. It will start on one side near the pointy end and end up across on the other side. At the pointy end you don't need to remove any material with your plan because it is fitting correctly there. At the other end you will need to remove more material. Take a couple strokes at the wide end of the taper, reducing the strip width there, and the one longer one to just remove the pencil mark. In this way you will remove more wood where more needs to be removed, but little or none where the width is good.
A very sharp plane will set at a very fine cut will remove material slowly allowing you to dial in a very snug fit.