Gidday Noddwyr,
To be honest, I liked your initial setup better: Multiple Wraiths, Carn Dum in units larger than 4, and Orcs rather than Spiders.
You definitely want Buhrdur, no question. However, and I run Carn Dum as my primary army, def 4(6) seems to need to be in larger units than the 3-4 I am happy to run my MT warrs as. The first reason is that many basic troops are str 4, so kill twice as many of them as they would kill eg MT Warriors, Morranans etc bow at shortrange also nets twice the kills vs these troops. The second reason is that these troops only pay for themselves when charging, and Ringwraiths (or any mastery 2 Darkness caster) are key here. Wings of Terror and Pall of Night are the most reliable methods to ensure you get those charges.
Orcs could be there to add variety. I may be a lone voice, but I rate 20pt bow highly as an efficient troop type (given they can also fight in melee) and 2HW Orcs can be deadly effective smashed in as a column, through carefully created gaps in your line. I don't run Orcs myself, but they are on my 'to get' list. It is a huge shame that Wargames Factory are having issues atm and I will likely have to put that off. I find that Mordor Siege bows (I've actually converted some with Carn Dum Crew) fit very well with the list as well.
The Tainted and Dwimmerlaik are both excellent Wraiths. The Tainted in particular has good synergy with Berserk chargers. He is a backup method (expect spells will fail at least once or twice every game) of preventing charges and can give each Carn Dum coy +4 dice in the melee. The Mouth of Sauron (to represent a Black Numenorian Lieutenant) is another possible option, but it gets trickier since he takes up allied points. Another good option is to use Thrydan's statline to represent 'the King of Carn Dum' or even the King of Rhuadar. His 'inspiring leader' makes a lot of sense here. I feel that his hatred of Rohan also maps perfectly onto the hatred the inhabitants of Carn Dum would have felt for the mounted raiders from Rhohavian.
Hope that helps.