Actually Bakker's style of dominance through internal dialog makes it easier to adapt than Martin's, you can retain more of Bakker's spoken dialog without having to go through the epic battles of condensing tons of ridiculously juicy wordplay that Martin excels at. You then articulate backstory through whatever creative way you can come up with (sexposition would be appropriate in this verse).
You definitely would not take a Malick route. Nor would you want to go the didactic manner of people speaking their thoughts, or a David Lynch/Dune esque 'interior dialog'. Rather, you rely on your actors to get across as much as they can, and you give them an assist with half a line or half a scene that straddles the line between implicitly and explicitly saying something. Audiences are quite good at following interpersonal dynamics, so scenes where characters are talking around something can be done quite adeptly--while completely supporting an internal dialog--given an adept utitlization of the basic dialect of television storytelling (meaning, anyone can cut a scene with a few meaningful looks involved).
And it helps that Kellhus, the person with the most meaningful inner dialogue because he's visually a cypher to the audience or is being directed and written to seduce the audience as well, has everything about him established through scenes with Leweth and Cnaiur where an otherwise inner dialogue can be relatively seamlessly brought to the fore. Since the other characters all deliberately wear their hearts on their sleeves, their inner dialogue will be written on their faces, and in the edit. A meaningful look of jealousy from Akka when Kellhus laughs at something Esme says will say as much in 50 frames as Bakker says in 5 paragraphs of Akka's internal self-recriminations.
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The real challenge is not in the internal monologue, the real challenge is plot, story and character disparation. The story is constructed in a manner that is extremely challenging for a television season. Looking at the story as a whole, you have two season ending events, Umiaki and Shimeh. You can't write a season of television that begins with a bunch of unrelated characters heading towards each other, and then ends when the characters run into each other in the last episode and have a pow-wow with the emperor. Oh my, that is dramatic!
The advantage, the brilliance, Game of Thrones has is that every main character of the first season is pretty much in one place for the first episode, and then a gradual dispersal pattern spreads from there as the sub-plots and characters fan out in all directions. The one exception is Dany, so you really only have two things for the audience to remember in the first episode.
A first episode of Prince of Nothing is a fucking plotting disaster. You start with a two-four scene prologue with the founding of the Dunyain then flashforward 2000 years. Okay, well make it a pre-credits scene and you can probably excuse it. Kellhus wandering the wilderness is a montage sequence probably not longer than 45 seconds, ending with him collapsing in the snow. Then you’re halfway across the world to Carythusal, and you’re wasting time establishing a location that will never be relevant to a single character in the rest of the entire run of the series. That’s expensive and absurd. You're also wasting time establishing Akka as a spy when he is never really a spy in any sense of the word (at least not in a way that would work on TV) at any point or any time in the entire run of the series after this point. Then you’re off to Momemn, to establish the emperor in a scene that establishes Conphas on the field preparing for the battle against the Scylvendie. We move across the battle lines to Cnaiur and establish him and that there is a power struggle for the leadership of the horde is going on. Then we move back to Kellhus and Leweth before zipping back to Achamian, probably now in Atyersus, so we’re brutally wasting time establishing him in a second location that will only be relevant one other time in the entire series. Since every character (other than Kellhus) has been mentioning that a new Shriah has been elected we move to another new location, Sumna, where Esmenet is established, hearing about the new Shriah from one of her clients. We switch back to a battle scene where Conphas outlines why the Scylvendie will fall to him (because they do the same thing) which segues to a scene of Cnaiur not being chosen (because he says they should not do the same thing) which segues to Kellhus telling Leweth that men always do the same thing, then the Sranc attack, Leweth exeunts, and Kellhus faces down Mekeritrig before fleeing, roll credits, end episode one.
The point of all that is that it's an order of magnitude (or two) more complex than the introduction Martin gives us. The struggles of plot Game of Thrones will face in it's fourth and fifth season are struggles they can afford to have because the show is at the height of it's success and has earned a bit of a downslope. You're asking Prince of Nothing to take on all those struggles from the very beginning. It's a hard sell without some significant changes. but I think you could minimize the changes. I'd seriously consider throwing out Xerius, though that would necessitate a lot of research into seeing how Conphas' motivations and considerations and calculations change if he is already emperor rather than heir apparent. And I'd consider throwing out Carythusal and Atyersus. I'd make Sumna into something more like Sauglish, the seat of power in the three seas, where The Mandate, the Scarlet Spires and the Inrithi faith all coexist in an uneasy truce (and have for millenia). You could still have Atyersus on a barrier island that leads to Sumna's safe harbor. This would also allow Sumna to become something of a foil for Shimeh, because the Inrithi have never allied with a school, while the ascendent Fanim faith has allied with a school (the Cishaurim). I'd also make Esmenet a lot more important early on. Yes she was a whore, but that just meant that she was ideally situated to encounter all three of the power players in Sumna, and she figured out how to leverage knowledge into security and safety of a stable livelyhood. I'd make Esmenet the spy, not Achamian, she trades whispers from one faction to another and that's how she really makes her living. and that's how she knows achamian, Geshrunni, Inrau and Sarcellus, they're all patrons of Esmenet's house of pleasure. I'd make Achamian, the noted (and disgraced) Mandate Scholar, the Mandate's ambassador to the Shriah, which is a ceremonial and useless insult position because there is no official contact between the Mandate and the Shriah, anymore than there is between The Mandate and the Scarlet Spires. There are unofficial contacts, naturally, but Achamian would never be privy to such, especially not after the House Nersei disaster. Nope, a roll of the whore's dice causes Achamian to get mixed up in everything, all he wanted was a night at the whore house, unfortunately, Geshrunni and his revelations fall into Achamian's lap.
