If I play Tomb-Raider Barbara and then cast Defy in response to a spell, leaving me with 6 runes, does Barbara still kill a gear?

Yes — Barbara still kills the gear. Her “if you control 7 or more runes” is part of the trigger condition, checked when the ability triggers, not when it resolves (Rule 383.2.a.1). Once it has triggered with 7+ runes, paying Defy’s power by recycling a rune and dropping to 6 afterward doesn’t switch the ability off; it resolves and kills (or disempowers) the gear chosen when it was finalized.

This is different from a resolution-time check like Siphoning Strike’s rune count.