Cory, I am no coach, but jumping on and off the treadmill (Example A) sounds like a recipe for low quality movement and mental focus drift to me. Why not do the two back to back or just decrease one to make room for the other if the total stress is too much?
From what I’ve gathered from UA teachings, if you have to do both strength and cardio, do them in that order. Doing the cardio first will compromise the maximum muscle recruitment you can achieve and the benefit of your strength workout. If you are not well fueled, your strength performance won’t be what could be.
Even tried bouldering after a run? It’s not the prettiest. I know we have to cope with the reverse order in the alpine (approach, then climb), but in training keeping it the other way and maximizing body freshness and mental focus seem desirable to make the most out of your session.
There is a really good discussion with Steve and Mark near the end (just before 50min?) of the 10/19/22 lecture recording that touches on your Example B above and in general how to incorporate extra strength/climbing work in a cardio/leg focused training plan.