For all those out there like me that struggled to figure out how to turn barrels on their sides the answer is impossibly easy... which is why it took me so long to figure it out:
Make a blueprint of a barrel. Use another blueprint to place the barrel and it becomes rotatable to almost any angle because blueprints of blocks can be rotated. You can even rotate a row of multiple barrels. I'll attach a single and a row of 4 barrels turned on their sides for anyone that wants them.