I put my body on the line for science!
Left foot first resulted in a safe descent.
Right foot first resulted in a cascading failure that ultimately had me heaped at the bottom of the stairs.
On ascent, it did not matter which foot came first, as long as I was climbing only one stair at a time. When switching to double stair climbing, left was the only option, as right would once again result in a cascading failure that would have me heaped in the middle of the stairs, then slide unceremoniously to the bottom.
Overall, I came to the following conclusion:
Science is always better with several pints ingested beforehand.