The technique for fitting the last piece is similar to the standard tapering method, except that you can’t fit the full size strip into the space available anywhere. Essentially you’ve reached a point where the taper from one end is overlapping the taper from the other end.
I started off the same way, cutting my piece precisely to length. Then I made a series of reference lines on the adjacent piece and on the strips. I measured the width of the slot at each line and transferred that measurement to the strip. I then connected the points with straight lines and roughed out the shape with a knife and followed up with a block plane, leaving a little material on the line. Then I started fitting from one end, using sandpaper to remove the tight points. I worked my way to the center and then started from the other end. Once I reached the center again, the piece was ready to install. I applied the glue and used small strip scraps hot-glued to bridge across the joint in a few places.