Ditto the Aqua Mira. Note that the real weight you should consider for a filter isn't dry weight, but the weight after you've used it (even if you do your best to get out what water you can).
Ditto also the question about whether this is for a thru, or at least long chunk hike, to which I'd add the question of when you plan to start, maybe even which direction.
Injinji toe socks: I've carried these on thru-hikes for occasional toe blisters, but only for those situations. The catch with these is that they're not that durable, I tend to wear out the ball of the foot in a pair of Injinji's relatively quickly. Something like a fox river brand liner sock lasts quite a long time in comparison.
In terms of whether the list is complete:
How do you plan to carry the iPhone? If it's your camera, you'll want it handy. Putting it in a pack pocket, or ?? I like a neoprene case hanging on a shoulder strap, with the phone in a snack-sized ziplock on wet days.
Stuff sack pillow: you're going pretty light on clothing; will you have enough to put in a stuff sack pillow? OTOH, pillow needs for a hammock hanger are a bit different.
In the context of how lean you're going in other areas, I question the need for rain pants.
Why camp shoes? For some at least (me included), just loosen the laces a bit so they can slip on and off and your trail runners are fine camp shoes. Hardly any creek crossings of note on the AT.
Hard to talk about clothes much without knowing when you're going, but some sort of mittens or gloves perhaps, at least liner gloves. Some sort of warm hat?
Some sort of pack liner, and/or even a very light pack cover --- it doesn't look like you're super tight on budget, so look at zpacks for a cuben one perhaps.
I suggest that you plan on carrying a plastic water bottle or two to augment your 2-liter platypus. On occasion this will be helpful to fill it with, and for me at least a 20 oz gatorade bottle is the only 'cup' that I carry.
There are a good few places along the AT where your water source is a fair slog downhill from a shelter. In that context, a second platypus with just a cap is worth carrying. And note that these aren't comfortable to carry uphill when full of water; consider an actual water carrier of some sort. Bringing more water to camp than I figured I needed helped me to rehydrate.
Ask your doctor if s/he will give you a prescription for, I think it's doxycyclene (in case you come down with clear Lyme symptoms). Mine did.
Purell, or the equivalent. Often no water around to wash with Dr. Bronners when you need it.
How do you keep things dry that you don't put in the hammock; hang underneath? A thin black plastic yard waste bag might be handy.
Sewing needle plus dental floss.
I find one of those really light pack towels worth the weight, or at least a cut-down square from one --- if for nothing else then to dry out your tarp in the morning before putting it away.
As light as you're going, and as close together as resupply points are on the AT, consider ditching the stove and eating cold. Food items aren't necessarily that much heavier going stoveless, and you likely won't need a lot of food per day when starting out at least.
An impressive list; if you think to do so, please follow up sometime and post the base weight that you actually end up using, and how well all of this works for you.