With help from my friend Rob, I finished the bottom tonight. Here he is hard at work.
I did a bit too, see here's proof:
Here I am checking the second last strip for fit. It is really just a long thin sliver. I turned a strip on edge, then planed it down to the right thickness to fit it in. Thus, it's about three times taller than the gap it is to fill. I think this worked better for this thin strip, partly because it gave me more material to hold onto and also ensured that the sliver would sit flush when trimmed.
One more gap left to fill:
Here Rob checks to see if his carefully trimmed strip fits into place:You'd think with a pencil that colour that I wouldn't lose it so often.
Here I am gluing the final bottom strip into place after Rob's careful trimming:
Voila! It fits!