I agree with above though and check out some safe routes and means of travel. Don't think I would really want to hitch through Mexico these days or for that fact any place in S America.
I would plan the route ahead of time and let some people know your itinerary.
I would not worry about what food you are going to initially carry because you cant carry enough to make a difference anyway over the long run.
You do however need to carry some means of buying what you need on the road.
Trapping/hunting/fishing, although it sounds great takes a lot of time, so if you are not staying in an area for a week or two, I cant see that working too well. You would be better off getting a job for a day or two and buying what you need.
Of the 3 fishing would be the best.
Odds are too low on trapping as you need to set 10-15 traps to increase percentage of game caught.
Hunting may not be always legal especially if you don't have a license and what will you hunt with anyway??
Hammock is good especially in the tropics if you want to stay off the ground, but guaranteed many multiple times on the trip you will not be able to hang and there will be bugs and lots of them. A tent is probably safer for the long haul unless you are used to hammocking.
You will constantly be buying, swapping and replacing stuff over the entire trip so have a way to get your hands on some $ on the road.
I would get a different type of stove that uses a more common fuel you can buy on the road like a white gas stove or an alcohol stove. Wood would work too.
Forget the hatchet unless you want it for defense.
A folding or collapsible saw like the little gerber is a much better and lighter tool. Besides if the police check you out the hatchet will probably be gone.
Make sure your bushcraft knife is within legal limits of where you will travel.
Paracord is good.
Forget the boots until you need them later.
Too heavy. Just take running shoes.
Change your sleeping bag setup to a 3 season + a summer bag.
You will need it up north.
Same idea but maybe start with a summer bag and pick up a 3 season on the road. No reason to lug around 2 bags all over S America and Mexico.
As far as food, forget the sack of rice and beans and tuna and count on re-supplying every 2-5 days. You should be carrying 2# of food per day.
You need some way to treat and carry water.
You need a lot of other things too along with mostly a solid plan. Didnt see any rain gear.
Depending on your route you are traveling from the Tropics, to desert, mountains etc. If you end up in the Pacific NW - wet and just plain soggy and cold.
AK can get freekin cold.
I have done long distance trips long ago similar only in the US and you run into many varied conditions and need to understand how to deal with them. IE I guarantee at some time on the trip you will get wet and cold and borderline hypothermic unless you are well prepared.
You really need a totally different set of gear in the tropics at your start from NW USA, Nw Canada and AK.
If you do end up in the NW USA, Canadian NW and or AK, just remember they have brown bears and grizzles, wolves, coyotes, Mountain Lions etc so handle and carry your food properly.
There are so many ways a trip like this could go bad that I cant even begin to count, but if you are serious, you need to do a ton of research and planning, and do some 2-3 week long shake downs.
Firstly to make sure you can handle it on the road for that long, 2nd to test out your gear. Many varied climate conditions on this trip.
On the road for that long, anything can happen at most anytime. My last similar trip was long ago. I ran into people that had been traveling for years.
We made it about 4 months and that was enough for me.
BTW I had a 0dF down bag, good pad, and a good tent and a Kelty Alpine pack and a lot of other good gear. The bag was way too hot for summer, but sure came in handy when it got really cold. We would travel for a while and work for a few days here and there, then off again. We traveled around the entire US from Florida to Washington State.
Have a safe trip and plan well.