How can I stockpile Harming II arrows?

You're best off with a witch farm, and a brown mushroom farm, and a nether wart farm. A general mob farm (with player killing the mobs) will be also helpful.

Witches will provide you with unlimited supply of:

• spider eyes
• glowstone
• empty bottles
• sugar
• sticks, if you choose to craft the arrows, or trade with a fletcher.

That's 4 of the needed components, and one useful materials. You'll also need Nether Wart, and brown mushrooms, and a couple blaze rods, and your potion situation is solved. Brown mushrooms are a bit of a problem - they grow very slowly and aren't easily found in large amounts, so an automatic farm for them is going to be big. Although you can grow them into giant mushrooms and these will drop more when harvested (with a non-silktouch axe) - for this you need bonemeal.

A general mob farm will provide you with spider eyes (witches don't drop that many, and you need 2 per batch), arrows, and bones -> bonemeal. Alternatively, you can trade sticks for arrows (32 sticks - 1 emerald - 16 arrows) with a fletcher.

If you decide to craft your own arrows, you'll also need a chicken farm (an automatic chicken cooker is a good source of these - and food), and visit gravel mountains with a Fortune III shovel (or just have patience placing and breaking gravel over and over).

After that, it's easy. Fill bottles with water, brew Awkward potion with nether wart, Poison with regular spider eye, craft sugar, spider eye and brown mushroom into fermented spider eye, brew the poison with that, and then improve with glowstone. Pour 3 potions into a cauldron and use a stack of arrows on it to convert them to tipped. And enjoy the surplus of gunpowder and redstone from the witch farm.