Speeding up complicated games by limiting player interaction
There are various ideas that I've used in the past to help. Be warned though - ultimately long games are long, and there's only a limited amount you can do about it.

1) Use a timer

Timed negotiation phases go back to Diplomacy. They're an official rule feature of Here I Stand. Not only does the time limit help the game along, and focus players, but it actually adds an interesting layer of strategy because you can't always talk to who you want to when you want to, meaning players have to work around it.

Only a few negotiation-heavy games feature a specified negotiation phase. But it's quite easy to add one - look at the turn structure and decide where it's best put and then enforce it, and the timer, with an iron first. 

2) Ban paper and mobile devices

As you've discovered one of the worst culprits for slowing down games generally are players who insist on making notes, referring to them and optimizing their strategies. Unless it's absolutely essential as part of the play that they be allowed to do it, ban the recording of anything on anything except for the officially supplied game components and enforce it with an iron fist.

3) Overlap wherever possible

There are a surprising number of games where players can actually overlap their turn structure to try and get things done faster. This isn't specific to negotiation per-se. In Titan, for instance, the meat is the movement phase. So after playing X is has finished moving and is recruiting, the next player in line can be checking their stacks, splitting and rolling for movement. Identify areas suitable for concurrent play in your game, and enforce everyone doing just that with an iron fist.

4) Play online

I never play Diplomacy in real life any more, because it takes too long. I do, however play by email. And doing so has given me a particular delight in the fact that I have to negotiate via email. You can't see the face, or the body language of the person you're negotiating with, which leads for interesting decision making. Not to mention that it's pretty thematic since early 20th century diplomats spent a lot of time writing to each other. The same is probably true of AGoT, except they probably write with iron fists.