Mojang patched out the glitch that my previous potion-tipped arrow making machine used... but no fear - here is a redstone machine for automatically creating potion-tipped arrows, with 100% optimal conversion rate and that can be used while AFK.

Input is done through two hoppers - one for arrows and one for potions. The machine will activate whenever it has 6 or more arrows and a potion, and losslessly convert those 6 arrows into potion-tipped arrows for the given lingering potion. It can be loaded up with a very large amount potions and arrows and then left to run while AFK.

This currently works in the Minecraft 1.9 snapshots, but of course there's no guarantee that Mojang wont change something, making it break.