Possible Clues:

• Particularly concerned about what's number one
• Acting in an extremely self-conscious way?
• Thinking of oneself foregoing, perhaps?
• Gregory is seen to be so self-centred
• Selfish guest finally interrupts flustered concierge
• Like old astronomical models positing that the sun revolves around Earth
• Self-obsessed fellow accepting money after game
• Like divas, and like the names at 17-, 26- and 43-Across
• Wrapped up in oneself
• Self-absorbed, say, with wild conceit about source of reputation