The same stairs that we fear and diss can be help I found out with first knee replacement. Surgery hurts for a few days, that eases soon. But, tig, what I discovered soon (my mantra) don't fall down. Even getting up from low seat, make sure the chair has arms. I've discussed this many times with rehab for both Ton and me. Getting up is worse than going down!
But those same stairs that make us cringe can be a saver. You just scoot over to stairs, especially down flight with railing, and do what you said - lower your feet to a lower level and pull up on railing. When I took my tumble in December I was on a flat slate floor, had to scoot about 4 feet over to the staircase, and then put my plan into motion. Doesn't help the pain and there was nothing broken in leg - but I could have been there for who knows how long. Got up via the plan and walked out to the garage where's there is a phone hanging right handy. 911 on way.
Also, as a helpful hint, and past bright idea. First was to eliminate the two steps at the front door. Broke down concrete and made it one slight slanted new pour so it angled right up the door.
Also, at that before mentioned garage, about 5 years ago we put in a grab bar at the inside right wall; there is one step there. If you think about it - moving grocery bags from the car to the foyer frees an otherwise unused hand/arm. May as well steady yourself.
Do we need to start a Helpful Hints chat? Can't wait to see your butt.

For sure you should check things out.
Mine would not be an anything special pic. Elbow/arm was almost blue/purple/black. Current issue is the wrist/hand.
P