Hi goirish
It looks like you have the right answer. Back around 1973 or so, when I began in this wonderful hobby, I had the same problem as you have. I was connected with a machine shop then. I had the machine shop make me a step drill. I am looking at the drill now. The first 5/8 length of drill is 1/4" diameter, and the rest of the drill is 3/8" diameter. I cannot remember using that tool much. I have a hand step reamer also, but do not recall using it in the past 20 years or so.