Switching shoes is probably the best way to find "injuries" regardless of going from stiff to soft or vice versa. Your body adjusts biomechanics based on what it's used to. The feet have a lot of mobility naturally which ends up affecting all the joints above up the the back when they start acting different from before.
Since you (and Daryl) both feel going downstairs is more comfortable when using the ball of the feet first, that sounds like biomechanics. Basically with stiff shoes you often get a lot of heel cushion. So you "learn" to strike with your heel since the boot absorbs the impact. When you get rid of that cushion, now your heel takes more direct force and that translates into your knee bits smashing into each other harder than before. Over time this gets tender and can hurt a lot eventually.
If you use the ball of your foot first, then the entire structure of your foot acts as a spring/cushion to soften the impact on your heels. The foot/ankle/calf is REALLY good at doing this, but only if it's strong. Making it stronger is not a particularly fast process. Muscles are slow to develop but I suspect that most people have weak tendons and tendon takes FOREVER to grow stronger. It's akin to developing finger strength in climbers…years of climbing is the only thing that works.
You can't just swap out boots for trail runners and expect to get the same mileage out of them. With boots you have to "break them in" until they're comfortable. Well with progressively softer shoes you have to "break in" your FEET! Start with day hikes and slowly increase the miles so your feet and ankles can get used to having stabilize more often than before.
Trust me, been there done that and now have a chronic knee issue (but will also never go back to overbuilt shoes).
In the meantime stretching helps a little. But surprisingly the most effective treatment I've found for knees has been exercise. Specifically a range of different two-legged squats and lunges in all directions coupled with single leg body-weight exercises and plyometrics. Think cross-fit type stuff but doesn't have to be as intense. It makes my knees feel stronger and more stable which over the long miles allows my knees to resist all the impact better.
PS: Trekking Poles also alleviate a lot of the downhill force and keep my knees to a dull ache instead of throbbing burn when I'm lax on my non-hiking leg exercise.