Gauging opinions - what is the lowest $ threshold per claim you would be happy with for the airdrop offers? 

Standard budget from teams is $10K -> 1.5K-2K users. Right now the amounts are often $5-7 which feels like a sweet spot in balance but open to feedback. The lower the amount the more users can be included

I feel the word airdrop has gotten stigmatized because it has often been associated with low quality or spammy projects.

Change the narrative to reward people who are actually putting in the work:

Claim
Bonus 
Reward
Gift
Boost