Mike, I've been thinking about this and I have another suggestion - although you have no chance of finding a new one.
A Giant Revive. These were designed by Mike Burrows, probably one of the most notable bike designers of the last century.
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It solves the balance issue in that you will always be able to get your feet down on the floor when starting and stopping.
They are hard to come by now but there is currently one on Ebay.
I would still choose an Electra Townie. It is also semi-recumbent design, in that the cranks are quite a long way forward of your feet although obviously not as much as the Giant.
With the Raleigh you have shown us above you will have to choose between having the seatpost high enough for efficient pedalling or low enough for both feet to be flat on the ground. Islabikes have a similar design but have solved it in a different way with a seatpost that rises up and down with a remote control (a "dropper" post). These are expensive but well-proven, as mountain bikers use them for death defying riding.
Still, it strikes me that the simplest solution is the Electra or the Giant. You have your legs extended enough for efficient pedalling but are still able to put both feet down. This is a very rare thing to find in a mass-produced bike.