Stairs can brutal, somehow. Doing staircase sprints even more so.
Regarding the blocking technique you're describing... I assume the elbow is also coming down and in, as the forearm is coming up? This is much, much more powerful than rotating the forearm up around the axis defined by the upper arm and elbow. Much faster, and easier to transition into a hold, lock or throw, as I recall (with a pivot or step, naturally).