In a surprisingly short time, I had the top plate shaped to almost exactly what I wanted. It is within a fraction of a millimetre in all the major axes. The perimeter still needs to be finished, but that will get done after it is thicknessed.
I mostly used the medium and small finger planes to get close to the desired shape, then scrapers to smooth everything out and make final adjustments. I really like using scrapers. They make accurate material removal easy (if slow), and leave a very nice finish.
I started on the bottom plate as well, but didn't spend much time on it. The maple cuts very nicely, but I expect it will take about twice the time that the top did.