You sound like you have plenty of experience, so this may be obvious, but do you tilt your bike sideways-- e.g., so the left side is closer to the ground than the right-- when getting on?
This is one reason I prefer lighter bikes. I'm 68 and 6" 1' (or 6" 2' on a good day) and 150 pounds with long legs, so I need a large frame. However, increasingly, when I stop at a light, or on the trail, or for any reason, I do so by angling the bike slightly to the left, and same when I get back on. But maybe this is exactly the moment when you are worried about losing your balance-- when you tip the bike fully upright and launch. My left leg has had three blood clots so I know I can't really trust it in this situation-- if I feel like I'm lifting it 10 inches off the ground, odds are it's only six inches off the ground.. So I stand on the left, tilt the bike left, and swing my right leg over the rear wheel-- the step-through vs. not step-through never even comes into play. My bike's top tube is JUST high enough that I can step forward to get off the saddle without having the excruciating thing happen, then I tilt the bike to the left side, and swing my right leg over the back wheel.
This only works because my bikes are very lightweight, of course. And this is why I'd never ride a motorcycle. They are too heavy. I remember having to re-park my buddy's Yamaha 750 when he was too drunk to drive, and it was terrifying. If the bike had leaned over more than 10 degrees from perpendicular, I would have dropped it for sure. Was a truly stupid situation-- he'd had about 12 beers and I'd had eight, and did not know how to ride a motorcycle. But it was in NYC, so all I had to do was make it across 72nd street, which somehow I did.
By the way, since no one else said it: Good on you for staying in the game as long as you can! Best of luck on the hunt.