my only other thought is that the last couple strips and short strips as you described are simply going to be the most complex, time consuming pieces you may make.....so patience, taking off/sanding only small increments, and a lot of test fittings.....and you will get there with a perfect piece.

another approach when both ends have to be tapered a lot is to cut the piece in half and have the two pieces join with a butt joint (in the middle) which is saved as your final cut after you have ensured the tapered ends fit tight. (each half should be longer than you need to allow for loss while doing the tapered ends) the butt joint/final cut is easy to control and by being left to last can be so tight and grain aligned (especially if same piece of strip) that it is unnoticable that you used that trick.

that said, there are also a number of techniques to make any small gaps disappear if your work is close but not 'perfect'.

howard