On canoe trips I bring more beer than gear, but for hiking trips, beer just takes up too much weight. Besides, hangovers don’t feel that bad when I’m in the woods for some reason.
I’m with you on the axe. Most of my camping trips only move camp a few times over the course of a week and winding the day down over a fire just seems right. Here’s mine
Last camping trip I took, I drank about half a fifth of whiskey and two bottles of Wild Irish Rose, over the course of five hours or so. The morning after, I killed about a whole jug of water in about 30 seconds.
I really love the end of There Will Be Blood for that reason - Daniel Plainview wakes up on the floor of his bowling alley after a long night of drinking, and the first thing he does is chug down a giant jug of water. I love that scene because it’s so universal, that intense thirst after drinking, but it never gets shown in movies.
Here is a physics/camping trick.
If you take a long cylindrical object (like a log) there is a “sweet spot” for holding it. I forget, its at something like 1/4, or 1/3/ or 1/5 of the length or something like that. I think 1/3 is the magic number for a perfectly uniform object.
Anyhow, if you hold the object there, and swing the bejeezus out of it against something else (like a tree )it wont hurt your hands. For a non uniform object, you can adjust your hand position up or down the length as you increase the swing force to find the sweet spot.
I used this trick many times to break some pretty big stuff. Of course be careful as to where the flying parts will be going once you manage to break it by swinging it agains something else.
Also on the log thing…you can lay a log of any reasonable length across the fire. When it burns through enough to break, slide the log up and repeat.
It’s interesting that a lot of attention is focusing on building fires. Here in the east (and most long distance hikers I know out west) don’t bother with fires. Their concern is cooking and they either use a white gas cook stove or small wood burning stove that basically takes twigs, no need for logs of any kind. In my experience, people traveling long distances like the OP don’t build big fires for efficiency sake (takes too long to cook) and for LNT (cutting, fire rings, etc). IMO it has it’s place but rarely in long distance hiking.
On a trip of that length I ususally bring a paperback book or something to stimulate the brain, usually just some murder mystery. Can be a life saver if you’re stuck in a tent. If you are hiking with others a small deck of cards.
The most important things:
Compass, maps, rescue whistle, mirror. You might want the compass and maps. You probably won’t need the whistle and mirror, but if you do, you’ll be glad to have them.
First aid kit containing: gauze and tape, ibuprofen or naproxen, preferably topical benadryl, tweezers, immodium, moleskin, bandanna, chapstick, cough drops, more moleskin.
Some food which doesn’t need to be cooked. If your stove dies you still want to eat.
Parachute cord, some carabiners, and knowledge of what the bear threat in the area is. If it’s recommended that you do a bear hang, do so. (speaking from experience, even baby black bears are really goddamn scary close-up).
Water purifier, or iodine. Don’t mess around with the nasties that can live in any water. Assume it’s a disgusting pool with raw sewage draining into it, because iodine-tasting water is much more fun than giardia.
Spare socks, liners, and laces.
Headlamp with extra batteries.
A paperback book to read at night.
Not a bad suggestion but a machete’s a better tool.
I’ll add:
Flint and steel. For lighting fires.
Whistle. For emergencies.
A couple of black plastic bags. For keeping dry things dry and wet things from making dry things wet.
Is this an episode of bear grylls?
Les Stroud 
And the good thing is it works for BOTH ends if you know what I mean 
bringing two tubes and not mixing them up might be a good idea.
Tampons and/or condoms, toilet paper, saline solution and vodka.
Keys to the motorhome!
Actually, the real reason to bring this is in case you get lost.
You simply spray it on you, wait for the hot girls to appear out of no where to tackle you, take care of business, then follow them out to civilization.
You might lose the matches. My flint & steel clips nicely onto the belt, and doubles as a pocket-knife and whistle.
if you’re in bear country, a bear-proof food container is easier than hanging your food over tree limbs.
(but I don’t know if it holds 10 days worth of food)
Personal survival kit.
Matches (those outdoor matches in a waterproof case, aka Storm or Waterproof)
tinder (cotton balls soaked in vasaline in a film canister)
Fish line, 2 hooks, a split shot
mirror
bandaids etc
mini-survival “blanket” (assumes you have a larger tarp or better one of those "Space Outdoors Blanket)
mini-poncho
small compass ( assumes you have a GPS or large quality compass also)
Small water btl with water pure tabs.
This should be carried with you whenever you are “just going for a little hike to see…” Maybe in a fanny pack or a cargo pocket.
And then a pocket survival kit too.
Knife.
Flint fire starter.
whistle
small keyring led flashlight
You can put all of these on one key ring. This should be always with you, even on bathoom trips.
Having earplugs out in the woods seems like a really bad idea to me. If there is an animal in camp, I want to know about it.
Aru: That chainsaw is friggin awesome. I think I am going to get it.
Personal preference:
In my survival kit, the emergency things-have-gone-to-shit-kit, I keep a magnesium block. Small block will start a lot more than a handful of matches, and even the best match can’t hold a candle (heh) to the fire starting power of a mag block. (Not that strike anywhere/storm matches shouldn’t be in the regular gear already, of course.)
Bahhhhh
Real men carry powdered thermite in reused 35mm film canisters
You don’t live in the terminally DAMP southeast do you?
If I am worried about being able to start a fire, I stick a lighter here, there, and everywhere. By the time I am without lighter, I am probably buck naked without anything else either.