Nice bike! I almost bought a Sekine in 1976, but when I got there they didn't have the size I needed (and they said they had), so I went to another shop and found a leftover Velosolex St. Tropez, which I still have and sometimes ride. No need to get a "modern" bike unless you want to get integrated brake/shift levers.
I agree that the saddle is too high. Even if you can pedal 150 without rocking, nearly full extension is not efficient. You might want to rotate the bars up so the tops are horizontal rather than the drops; you could then lower the bars and ride the tops or hoods, and get low on the drops when needed. Also, I would check KOPS to locate the saddle fore and aft before thinking about changing stem length.