How about making your own barrels?
Start by getting a wood dowel (or a broom stick, etc if correct size) the diameter you want and cut off the length you need squarely. Use a tri square metal ruler with a center finder and mark the center of each end. Drill a small pilot hole through the exact center of your piece. Drill it out to fit a 2 inch long bolt at least 1/8 inch dia. Place the bolt in the center of the the piece and add a washer and nut and tighten it down. Mark up the piece where you want the slate hold down grooves to be to make it look like a barrel. Also make a cardboard cut out to use a pattern of the groove you want.
Place the extra length of the bolt in your electric hand drill or drill press if you have one. If a hand drill, figure out a way to hold the drill on a bench or in a vise wrapped in a towel. Use knifes and/or small metal working files to be held against the drum piece in the running drill and carefully let the files remove extra wood to make the piece into a drum shape. Use fine files and sand paper against the spinning barrel to finish its shape.