I'm in the same situation with drop bars: "My neck don't bend that way no more." I'm prone to tweaking some nerves in my neck, and want to avoid the danger zone while riding.
Twitchy means that the bike is highly responsive to control from the handlebars, making it much more maneuverable but also perhaps a bit unnerving to the casual rider. Two things. First you quickly get used to a twitchy bike, and second, our kinds of bikes start out with much more stable geometries (having to do with the angles of the steering tube and fork) to begin with. I've not experienced a problem with any of my bikes. One is essentially a sporty-looking hybrid, the other an old Schwinn road bike frame built up with odds and ends from the bone yard.
In addition to the wrist angle and higher posture, I also like my hands further back so I'm not reaching out as much. And further adjustments are possible. On my yellow bike, look how short the stem is -- the handlebar is barely a couple inches forward of the steer tube. Some bikes, you can flip the stem so it's pointing upward rather than downward. There are steering tube extenders. Lots of options. At some point you might find that the cables aren't long enough for further adjustment unless you install longer cables.
Indeed, I've noticed that the marketing pictures always show bikes with high saddles and low bars, but when you see guys my age on the same bikes, they've always raised up the cockpit.
Thanks so much for this detailed info! My bike tech guy, who sold me the Orbea and put the new handle on it last year, told me that he doesn’t recommend extenders. He also said I had a limited amount of raising I could do before I’d need longer cables. But I intuitively like the look of the bars on the red bike in your pics. It looks like that wide, swept grip would be very comfortable. Between it and the other bike with the shorter bars, which one is less “twitchy”?