BW exercises for core is amazing.. add some stability stuff to it, and wow. That's really all you need for an amazing core.
Yea, I figured it was sitting because that a single-jointed exercise, meaning that the elbow is the only joint absorbing the energy. With multi joint exercise, like standing barbell curls, you can absorb some energy with the ankles, knees, hips, elbows etc. But as you said.. you can kinda cheat with standing by using your back to bring it up ahah
That being said the singl-joint exercises are fantastic for targetting a specific muscle group. When your elbows feels better and you're back to doing those, I'd recommend slightly less weight, but squeeze at the top and serious control on the way down (aka negatives). That'll really give your biceps a blast!!