You seem to have most of it covered, by the time you have been on the road for a bit you will realise that a lot of it you can do without. Before our first LEJOG 3 years ago my friend and I planned our kit as much as you did.viewtopic.php?f=16&t=48438
Here is the thread.
Whilst much of the kit that you see as being very necessary, the pillow for example, will also add weight. I have found reducing the weight has increased my enjoyment of the cycling significantly whilst allowing us to cover greater distances at greater speed. Your cooking kit seems like there there is a lot of extra stuff that could be doubled up. For example I use just a basic swiss army knife with a can opener, a corkscrew and blade as well as a spork. Whilst most days we don't end up eating much more than pasta we normally do have a few extravagant days where we eat like kings. The bottom of the frying pan can be used to chop veg etc or just cut it directly into the pan. When you finish cooking just eat out of the pan as well, saves washing up and means you don't have to carry a plate. The pot cosies can be useful and might save you some fuel they do add weight and bulk, a windshield like this http://www.cotswoldoutdoor.com/primus-c ... colour=180
will save more fuel and clips round the gas canister, the frying pan doubles as a lid and will also save fuel it can also be used to drain stuff from the pan. It is always worth having a spare source of fire, I prefer lighters as they are more reliable but carry a spare.
Clothes wise why take a bandana and a scarf when a buff does both? Also no trousers?
On your wash kit don't get caught out and keep your toilet roll in its own airtight bag, thats the last thing you want getting wet when the rest of your stuff leaks everywhere. Suncream I recommend P20, you only have to put it on once and it lasts all day, it smells a bit but means you don't have to stop to put more on all the time. Make sure you know how to use the stuff in the first aid kit, I normally add one of those foil blankets, some matches or a lighter as well, you never know. The water sterilisation tablets are dead useful especially if you end up wild camping, just make sure you realise their limitations. They won't kill certain types of amoeba, normally Giardia and Cryptosporidium, unless you have chlorine dioxide tablets. You shouldn't ever be far from clean water anyway though.
When it comes to your tool kit make sure you know how to use it. If you don't know what its for for example the quick links, its probably not worth taking. I wouldn't bother with spare brake pads, you can replace them en route if you need to. It might be worth taking 2 spare tubes, you are away for a while and it is a nightmare fixing punctured ones at the side of the road is its your 2nd puncture of the day. I also take a rag and a small bottle of chain oil, I wipe down the chain to clean it and oil it every few days. This is a section that you can probably afford to cut more stuff, you'll never be far from a bike shop, as long as you can get there they can sort all of your problems.
You are carrying lots of food, I normally find its fine to just buy on the day or stock up for a few days, remember you are carrying it all. The most important piece of advice is to keep track of the day of the week, Everything closes on sunday so be prepared. Why take hair dye, if you really feel the need buy it when you need it.
The most important thing to remember is that the lighter your kit it the easier it will be to cycle and the more enjoyable it will be. 13kg is a lot of weight especially when you start going up hill. Factor in that you will be carrying water and extra food and snacks, it all adds up. This is our kit from last year, we packed in a hurry and ended up need ing an extra fleece each when we got there but that was fine. https://docs.google.com/spreadsheet/ccc ... _web#gid=0
Compare it with yours and see what you think, this year we are going super light and using bivi bags and not bothering with panniers, but thats an entirely different story.
Good luck, enjoy your ride and feel free to ask any questions.