Waterdeep:

Story Points: OK, so the cultists know that the characters are on to them, and possibly the Harpers and Zhentarium via the characters.

• First goal - Kill these characters before they can share the goals of the Cult. If that fails, kill everyone the character's told, and the characters to boot. 
• Second goal - Get word to the Roadhouse and Rezmir fast. A few riders are sent to tell Rezmir about the stolen shipment, with descriptions of the characters. Azbara Jos leads these riders. 
• Third goal - If killing those who know fails, the cultists in Waterdeep try to con the characters into traveling to the Roadhouse, where an ambush awaits. They let someone get captured who then "informs" the PC's in exchange for survival, etc. This ensures the character's know the path to the next chapter. Even more fun if they "sneak to the roadhouse with the shipment to pretend to be cultists" as this gets the loot where it needs to go (for the Cult).

The Roadhouse: 

Story Points: By whatever means the characters get here. They should be walking into a basic ambush. Capture or kill orders from Rezmir. On the side of advancing the story they need to discover the trapdoor and path to Castle Naerytar. 

• First Goal: Set up an ambush for the characters. The folks at the Roadhouse should let them in, feigning ignorance, and then trap them in the inner courtyard. Redesign the encounter to build a hard encounter via the list of NPC's at the Roadhouse. Cult of the Dragon Loyalists.
• Second Goal: After this encounter, the Lizardfolk arrive to transport the caravan's loot for the Cult. Finding nothing they get confused, seek out Bog Luck and encounter the characters. This could be a good non-combat encounter to learn about Naerytar if the PC's aren't murder hobos. If not, it should at least lead them to the passageway the lizardfolk use to get to the strong room at night.

Castle Naerytar:

Story Points: This should be a slog. The "bad guys" should know the characters are coming. Rezmir should have ordered the Lizardfolk and Bullywug's to capture or kill the characters on sight. If the PC's have behaved and didn't kill Snapjaw they should have a fair chance to get the Lizardfolk to rebel, distracting the Bullywugs and making this easier. My players did this.

• First Goal: PC's charge the fortified castle. Get rid of the weird encounters (undead, etc.) and focus on the humanoids there. You've got a several named NPC's with motivations, fun abilities, and the knowledge that someone's coming to disrupt them. I'd have Rezmir already gone, same for Jos. Use Pharblex and Dralmorrer as the "leaders" for this fight. Their orders are to kill the characters, recover the goods (if possible), and make sure nobody gets to the Hunting Lodge.
• Second Goal: Re-rationalize the castle. A head on assault will kill your characters. Sneaking to the castle, causing a Lizardfolk rebellion, and then striking at the leaders gives them a chance. If you are using Snapjaw, have him stress how strong the castle is (else he'd have attacked before). This is where your stealth characters can thrive, doing recon to set up the best attack.
• Third Goal: Do not let the module as written get in the way. Again, it'll steamroll the characters if you have them open every door and fight everything (intelligently). Instead create a few focused encounters to let the NPC's shine and do their job, and then tame the rest of the castle. It does not have to be hours of opening every door. After Pharblex and Dralmorrer are handled, have the forces fade into the background as the Lizardfolk take the castle.

The Hunting Lodge:

Story Points: Rezmir and Jos got here first. That means Talis knows. That means the Troll knows. Have the troll minding the portal landing to ambush the party when they arrive. Have Talis first welcome them into the Lodge (she sees the opportunity to advance herself still). Skip the people in the kitchen and kobold servants. They are a boring distraction. This is a troll fight and then 50/50 on roleplay or combat with Talis.

• First Goal: Trolls are scary. If your characters didn't rest before coming to the Lodge this could be a messy fight. Let that happen. Again, the bad guys know the characters might come. Your paladin triggered this. Let them have a real fight with the troll. It should be scary enough as is.
• Second Goal: TALKING with Talis. She's an opportunity for characters to realize that they don't need to kill everything. They need to talk, consider strange alliances, and then decide if they can (paladin morals). 
• Third Goal: If they go roleplay, Talis should let them know the castles about to take off. Parnast is boring, it should only serve as an attempt to distract your players, but they should feel a countdown to the castle taking off. No shipment is about to arrive, so it should be leaving NOW. She should encourage them to quickly race to the castle. There's a tapestry that will teleport people into the nearby woodlands. Repurose this (it just random as written) as a 'short cut to the edge of Parnast." to help fuel the urgency.

Parnast: 

Story Points: Parnast is boring. As the characters come through, the Cultists in town know to anticipate them. They know to stall them. They know the castle has to get away. So they should be more friendly than written.

• First Goal: Warmly welcoming "weary travelers to our quaint mountain town. Be sure to try the hard cider at the tavern. It's the best you'll ever taste." and whatnot. If this works, the players need to find the wyverns (let them) to catch up to the castle.
• Second Goal: The last effort of someone in town is to race ahead and warn the castle. Any fights should not be life or death for the NPC's. Just stalling tactics. Hit and run. Cause a chase into the woods. Anything to get the players off track. Again, if it works, there are wyverns. If it does not, it fuels the urgency and 'race the clock' setup that Talis gives.

Skyreach:

Story Points: Honestly, as written this is too much. Cull it down to critical encounters. The Giant. The Dragon. Ogre Guards to stall and delay. Get rid of the Vampire (adds nothing to the story), and the kobold kitchen, visiting giants, etc. are table dressing. Not combat encounters. The goals here are for your players to discover the story of the Giants in the Castle, and to foil the Cult of the Dragon Queen and Rezmir.

• First Goal: The Ogres are distractions. Make sure they are easy encounters, used to burn resources but not to deliberately cause death.
• Second Goal: Blagothkus. Open this up with a monologue if possible. Change what you need to do this. He's smart, wise, and capable. He should see the adventurers for what they are (agents of change) and make intelligent decisions. Either doubling down to help the Cult, or pivoting to use the adventurers to cause different chaos in the furthering of his personal goals. Just as your players should be deciding "Is this combat or not?" Blagothkus  should be having the same internal dialogue with himself. 
• Third Goal: Rezmir and a White Dragon terrify your characters in an epic final battle. This is why Blagothkus is a 50/50 encounter. He's scary, but also eats a lot of resources. Fighting him won't feel heroic. Not compared to killing a major leader in the Cult of the Dragon, while killing a Dragon. That's how you close out an adventure! It's epic! It's HARD!! It's fun!!!
• Fourth Goal: Jos is another 50/50 moment. If he's in the final battle it's very challenging (Rezmir locks down fighters, Jos and the Dragon opportunity strike, etc.). If he's not, have him mentioned in a jouranl from Rezmir (or something similar), and leave hints about the Rise of Tiamat follow on adventure. He isn't mandatory here so it's about combat balance as a decision for that final encounter