Updated lists:

KAREN BRYAN-DAWSON (8 titles, 8 confirmed)
- Fleming: The Man Who Would Be Bond (confirmed by AiAustria) Or does the UK suffix in her "Hair & Make-Up (UK)" credit make it invalid?
- The Hour (confirmed by AiAustria)
- Moon (confirmed by T!M)
- The Mystery of Edwin Drood (confirmed by AiAustria)
- Sahara (confirmed by T!M)
- Spies of Warsaw (confirmed by AiAustria)
- The White Queen (confirmed by greyghost)
- Without You (confirmed by T!M)

KAREN DAWSON (7 titles, 5 confirmed)
- Baby: Secret of the Lost Legend (confirmed by T!M)
- Dinotopia (confirmed by AiAustria)
- The Hit (confirmed by AiAustria)
- Jesus Christ Superstar
- Muppet Treasure Island (confirmed by T!M)
- Victoria Wood: Screenplays
- What a Girl Wants (confirmed by greyghost)

KAREN BRYAN DAWSON (2 titles, 2 confirmed)
- From Time to Time (confirmed by _ppj_)
- The Hour (confirmed by AiAustria)

KAREN DAWSON-HARDING (1 title, 1 confirmed)
- Oklahoma! (confirmed by AiAustria)

KAREN DAWSON HARDING (1 title, 1 confirmed)
- Great Performances: Cats - The Musical (confirmed by AiAustria)

So "Karen Dawson" can't catch up. Even if you want to dismiss the 'Fleming: The Man Who Would Be Bond' credit, it'd still be a tie, with the larger number of profiles acting as a tiebreaker. Either way, Karen Bryan-Dawson is the common name for now.