There's actually some advice in this section - so do search on this stuff - there have been some people who were asking about the same thing as well as input as to kind of bike, tires, etc - so there is some info there (someone recently asked too at beginnning of Summer-ish - but in that thread I posted a bunch of links to bicycle forums where long distance bicycling was the topic - I'm tired tonite so I'm not looking but they are there )
... but I'd balance out that bike - front end - I've been out several times but from 3 days, 5 days and an on and off 2 weeker (meaning that I stopped for a bit here and there) - nothing as epic as you are doing <bows> And an unbalanced bike is annoying. Come to a stop and the back end just wants to go down. Plus it makes for a more enjoyable ride to lightly balance out front and back panniers or similar. My traveling bike has front and back panniers plus a bike rack over back tire (makes for a great rain barrier too) with a small bike trunk.
There is another member here, @Kate Westcoast who is a big timer long distance person. Another source is a friend of mine from a bicycle forum we're on - @azcyclist who does ultra bike races (like 24 hr races plus 240 miles in a weekend) year round - he's in AZ so he may have some tips on hydration and food as well.
If you don't go for a bike trunk - do yourself a huge favor and go for a perhaps $20 or so and get some removable front and back bike fenders - man alive they are great when it's pouring on you. You avoid the black grease streak up your back and the black splattered face in front.
Get some good cheap glasses too - that's what I buy - $5-8 bucks at the bike shop - glasses - I break them (screw those $$ ones - do you know how many I've have dropped and either I or a car hammers them? hehe keeps the stuff out of the eyes - rain and bugs. Been splattered with way too many big juicy bugs). Get some yellow tinted too - they are awesome in the rain and at sunset even at night.
Just don't overload yourself though - that makes for a miserable ride hehe (I've done that using front and back panniers coming from public market - wtf was I thinking of 12 ears of corn, bushel of tomatoes etc etc - I hated everything when I came home). LOL I was traveling into Toronto and we went by one stretch and there was a guy traveling on the other side of the road. You COULD NOT see his bike at all. He had a huge overloaded big backpack on, enough loaded black garbage bags that you could not see his bicycle at all - had some panniers too - and he traveled very slowly and nearly painfully (to me).
Travel lightly - but with necessities - you'll always find. Just keep an eye on the water and carbs.
Brother's done cross country - he trained - with fully loaded front and back panniers with all the telephone books he could carry - and was doing I'd say 50 miles every other day or so (he was living with Mom when he got out of the service) - he trained cause he was going to hit mountains as he went the north trails. He packed a small (very small) tent and some clothes, bicycle clothes (they are light weight and dry quickly), rain gear, tools, spare tubes of course.
He had a very small single burner stove that he heated water for coffee, soup, ramen noodles, mac and cheese and beans - he concentrated on high carbs - therefore lots of beans, oatmeal with added dried fruits.
Know your routes too - know where your water is, bike shops etc. He also had very good luck with pot luck suppers at churches and I guess cause he was traveling solo - he had good luck with people inviting him to camp in their yard and to have supper. He had a great experience with that trip. Ended up traveling faster than what he anticipated - towards the end he said he was doing an easy century a day several days of the week. He was also in touch with my Mom who would send off supplies to him (including money at times - but he traveled quite lightly with little money) at certain points to a post office. Hope this helps.
Keep people at home appraised of where you are and where you plan on being and check in too. Do keep in touch here - being really on the road versus in a car enables you to see lots more of the environment and cool things out there. Pics please - and be safe and do have fun!!