When you said the hard way I thought you were going to be riding through Norway and not taking the easy way through Sweden...
2871 miles ... in 25 days... in winter.... 114 miles per day (no days off) do you think this is ummmm a bit unrealistic? I have been that way (in summer mind) and its a long way.
Looking out the window, its snow on the ground, so frozen ice roads. I cant see this changing over the next few weeks - hence the fat bike I suppose? Do you have
studded tires on it?
Going to need them - just not until you are in Sweden, so will be warn away to nothing if you are riding from Manchester to Stockholm! The roads are not always the soft loveliness in your picture(on your blog) but when the wind gets on the compacted snow, its just sheet ice.
You may have issues with the Nordkapp Tunnel (it has automatic "doors" in the winter... google it) but its also not a nice ride with 10% down and up (240 ish m subsea) makes an interesting, just not pleasant ride! I dislike riding in the tunnels over here, mostly (in Norway) you are banned and have to take a longer detour (the old road in many cases) but "up north" with the lack of traffic you can ride most of them anyway. Its an experience riding then I can assure you (if you haven't already done so).
Mostly thought, I hope you like trees... your route has lots of trees.... more trees than you can shake a stick at.... oh and some more trees. You may end up thinking Sweden is just trees... Then all of a sudden, no trees and a wind that can cut you in half as you hit the arctic proper.
All I can say is
RESPECT for attempting to do this in the time limit you have set yourself and please do not underestimate the cold and how dehydrating it is.