[Buffalobob]

Can this be accomplished successfully?
Sure

Do you accept the challenge?
Sure

Where do you start?
Charleston would be fine.

What route do you take?
Start at Charleston and go west toward Atlanta and then Birmingham to Texarkana and Red River into Texas to San Juan River to Colorado River to California. Being from the south the first part of the trip is easy for me to make and as general rule the Indian tribes were peaceful. The eastern Texas tribes were also agricultural and peaceful.

Where do you plan to finish?
Lower California between Long Beach and San Diego depending on what route can be found with water available every two days of marching.

Take my time and set the rendezvous for the latest possible date but get there early and wait in sunny California

How long do you think it will take you?
2200 miles straight line equals about 3000 actually traveled
8 miles a day gives 380-400 days
I think I would start in March. I would be into the Mississippi delta by early autumn and the River crossing would be easier but I would have to face winter out on the western plains.

What is in your field gear?
Beside things I mentioned in other answers I would take the following
Leather sewing kit
Six pairs of sox
Hat with brim
One complete change of pants and shirts
One pair of modern boots and one of high moccasins capable of being resoled

What modern items are critical, and what items from the period will work for you?

Backpack
Water purification device
2-Tarps for tent
Fishhooks
2 Titanium pots
Synthetic fill Sleeping bag
Space blanket
Synthetic thread, twine, rope.
Fire starting gear
Monocular or telescope
First aid kit with modern antibiotics
Two 5 qt water bags and two one quart hard canteens.
A small amount of gold for trade with the Spanish but the steel arrowheads and trade knives would be more versatile for the natives.
Couple of dry bags for stuff like ammo
Calendar device such as a watch. Need to know day and month in order to stay on schedule.

What are your priorities?
Water is critical once one gets into the plains and desert regions – Say west Texas to California. The object is to get to the Pacific Ocean so the lower California crossing has to be reviewed very carefully for water sources.
Snow storms in the western states - one must be prepared to survive them,
Safe river crossing are important to not getting hurt or losing gear in the eastern leg
Staying healthy and not pushing too hard and fast.
My plan is to pack about 8 miles per day which will take about 4-5 hours. Cook one meal per day in the evening and use leftovers for breakfast and lunch. So I would have about 4+ hours for hunting/gathering and gear repair and camp chores.

How will you carry it?
Expedition sized backpack if allowed (the term “period luggage” might mean a wood frame pack which will be a bummer but easier to repair if something breaks).
I have a wheel cart that I use often when hunting and it is useless without a good trail so I have no inclination to take something like that.

What firearms will you take?
I would take a folding carbon fiber stocked Volquartsen22 mag with iron sights and carbon fiber wrap barrel. 500 rds of ammo = 5pounds and that’s about one bullet a day. MV is about 2000fps.
Only two animals that would present a problem are the two species of bears and if you get into a fight with a bear you just got a major problem no matter what firearm you got. In a fight with hostile people, the rifle has accuracy and killing ability beyond what the opposing force will have. Of course you will be outnumbered but it won’t be the first time so that is nothing new. “Used for self defence in a revolver, the .22 WMR has compiled a 42% one shot stop rate according to Marshall and Sanow”
Wolves, mountain lions and other large predators get the majority of their food from small game and that is my plan. Small game is more plentiful and easier to kill and cook. You spend all day killing a buffalo and then days drying meat as opposed to just whacking a rabbit and moving on. If you move along waterways then you will have opportunities for fish, waterfowl, rabbits, etc, plus big game.
Killing a buffalo, moose or large elk can be done with the small caliber if one is willing to spend a couple of days at it. All that is needed is to take one rear quartering shot into the intestines and not spook the animal. As the pain gets bad it will bed down and then after 6-8 hours peritonitis will take over and you walk up and finish it with a knife- BTDT. Fooling around with a large animal and trying to dry meat and tan hides for new boots will be a very time consuming and labor intensive effort and you can’t carry much meat anyway. The only real reasons to kill a buffalo is if you need the neck hide for boot soles or if you are holed up over wintering. A dry buffalo hide weighs about 25 pounds and occupies about 2 cubic feet of space or more. Probably will need to stop for two or three weeks in the late fall to refurbish boots and clothing with tanned hides – hair on and off.

I would take string suitable for a bowstring (nonstretch) and if necessary build (which I know how to do), trade for or steal a bow and make arrows. I would need to do a little research on trees suitable for bow wood along the route. But as long as the rifle was working and ammo supply was good I would not carry the extra weight. I might carry about 50 steel, 2 blade broadheads as I don’t think I want to learn how to nap flint and you need weight forward on an arrow.

How much ammo, accessories, etc.?
At least 500 rds and perhaps another 200 if it will make the weight limit. Four magazines of 9 rds each. No cleaning gear.

What edged tools do you take?
I am not expert on survival type knives, but I would guess the current Harsey/Reeves SF is a good general purpose knife. I would ditch the scabbard as being too heavy and sew me a light weight one such as I make for my butchering knives. I would add six trade knives and leave most of the gold behind. I would have to research taking a stone versus finding suitable rocks for sharpening.
I have used folding saws a lot and they are good for the weight and I might carry one for building rafts until I cross the Mississippi River. It would be high on my optional equipment list.

What navigational aids do you take?
Duplicate set of water proof maps and one compass. Map scale would be 1 inch = 10 miles which would give me a 30 page set using 10 inch by 10 inch paper. I would mark alternate routes and checkpoints for schedule conformance

What do you think your odds are of successfully completing this journey?
95+%
Other than bad luck I think the need to have a balanced diet and avoid nutritional deficiencies is going to be the most difficult part.
I spend a couple of months alone every year in the mountains so I pretty much understand individual effort and being alone.

What do you do in the 30 days before you leave?
The one thing I would study would be identification of edible plants. My knowledge of them is very weak. Getting meat I can do but vegetables/berries would be a challenge. Second I would relearn Spanish. Review first aid and common diseases. Read up on basic leather craft for boot and moccasins, Finally, I would review the route in great detail because the San Juan/ Colorado River legs have a lot of vertical terrain and one would need to have that part well defined. Also lay out a alternative route through the Spanish settlements. Get in shape for a heavy ruck.