Your approach should work. The XP for each encounter is calculated by adding up the XP for each individual monster.
For instance, in the first encounter with 2 unarmored goblins the total XP is 270 (2 x 135 XP for each goblin).
You'll find that XP and CRs are a rough guideline and not an absolute science. For instance, an unarmed goblin is worth as much XP as an armored one, but one is a little easier than the other to hit.
You can also do things like add a few more hit points to the listed monsters or give them equipment.
For the treasure you can do the same thing you are doing for the creatures--add 20% for 5 players or 50% for 6 players.
Good luck.
I'll tell you a secret. You can adjust on the fly. Start out with 2-3 goblins and if your party plows through them, have 1 or 2 more spring out. If things go rough for the party forget the addition.
No matter how any designer or DM tries, no encounter plan is going to be "perfect". Eventually you'll get an idea of what your players and their PCs can and can't handle. You'll also have a sense of dramatic flow. I mean, do you really want the party to be wiped out in their first session, in the first 10 minutes because of encounter design or bad dice rolls. While some people may say that
Rarely, I mean rarely, you may have the PCs be dramatically rescued by the arrival of an NPC or an unexpected retreat by the bad guys, but if the PCs were the ones who got themselves into trouble (maybe by calling the Prince a loud-mouth) and not just ambushed by surprised, don't pull any punches!
I'm not saying to always do this, just keep it mind.
When I ran the adventure with my group, I really felt like it might have been made to favor new players with a feeling of superiority. My 12 year old son playing the wizard didn't truly face any problems, even when he swam out alone to the reefclaw island.
However, definitly play up the dragon dropping in to the room at the end out of nowhere, make sure they set their characters up before entering. When black fang showed up in my game, he rolled the highest initiative, then blasted both the fighter and the BB barbarian with enough damage to drop them. Seeing my first time players give each other a "holy carp" look and then buckle down to take it on, truly a great moment.
For two reasons:
1) While the rogue is dealing with the trap, the other party members are technically on guard and better able to react to threats than the rogue, so they are participating in overcoming the obstacle.
2) If the fighter gets a lucky crit, rolls max damage, and kill a monster before anyone else gets a chance to hit it, you don't award the fighter all the XP for that monster. Likewise, just because the rogue is the one who deals with traps doesn't mean the rogue gets all the XP for a trap. Likewise, just as the wizard tends to have ranks in Knowledge (arcana) and is the one who figures out strange magical runes that open a secret door, that doesn't mean the wizard gets all the XP or treasure for what's behind that door.
Basically, the PCs are a team, and they share the rewards, even if one person handles the brunt of a problem. In fact, a good adventure should give every character in the party the opportunity to be the best at something, or have the expertise to overcome a specific challenge that the other PCs would have a hard time with. That way, everyone gets to be awesome at something and contribute to the party's success.