Why are all the bonuses white? The reason for them to have colours is so you can distinguish them from each other easily. For this map you could, for example, have all Confederate states have a bonus colour that is a shade of red. All different of course, but that would make it better. And the same for the Union, but with a different colour.
And about the borders: this map has only 43 territories. It's not that hard to make the borders better, you just have to know how to do it easily. I will do it here for you, and then you do the same.
Step 1: finding a right background
I'm not sure which you used, but the highest quality image I could find was this: http://tripleadev.1671093.n2.nabble.com/file/n3120239/usa1860_big_colored_v2.png
This step also includes resizing it so it won't be too big at the end. I gave it a height of 1000 pixels, that's about right. And don't forget to resize the map viewbox so it fits with the image.
Step 2: tracing the outline of the entire map
Draw a path along the edge of the map. That can be done in 5-10 min.
Once you're done, you have a single path of about 500 nodes (depends on how detailed you worked) covering the entire USA, i.e. all the stuff you want territories to be made from.
Step 3: distinguishing the bonuses
In this example I'm going to show you me doing it with California, but the same can be done for every bonus. In your map, every state/territory is a bonus, meaning that you must do this for every state/territory. Clear, right?
Step 3a: trace the inner border. Make sure your starting and ending points are outside the territory you're dividing, Inkscape works that way.
Your finished result should look something like this:
Step 3b: divide the path. Select the path you just drew, hold shift and select the big path on the background you drew earlier. Now you have both selected, press CTRL+/ and your bonus is separated from the mainland! If you try to drag it away, it comes loose! (press CTRL+Z afterwards though). If you zoom in on the border, you see they perfectly overlap.
Step 3c: repeat steps 3a and 3b for all the bonuses (i.e. all the states/territories of the map).
Once you're done, you can remove the background image. It should look like this.
Step 3d: Now you have all the bonuses separate, but the borders still overlap!
That can be altered easily.
First, you must edit a setting to make this method work. Go to File->Inkscape Preferences, in the window that opens select Steps from the list to the left, and change the "Inset/Outset by:"-value to 0,35.
Now close the window, and select everything. Then, press CTRL+SHIFT+9, and watch the magic happen.
Now the borders still overlap, but a lot less than they used to, and there are no gaps (except for a few at the cornerpoints, but they're really tiny).
If you select all territories again and set the opacity to 50% (the number next to the O on the bottom-left), and zoom in on the border, you can clearly see what has happened.
Now you can put some flourishes on it if you want, and of course the bonuslinks and such. You know how to do the rest of it.