How can I obtain more feathers?

Short Answer:
Best reliable way to get feathers is grind in the Arena. No indication that level affects feathers. Participating in limited time events, such as a Voting Gauntlet is also an excellent source of feathers. You can also get feathers from hero merit, up to 2000 per hero.

Long Answer:
I've found useful information in the guide here or here (they're very similar), but I think you've found almost all sources of feathers, although you didn't mention quests. I've included relevant tables for feather values at the end of the answer.

• Tapping on friends - Greeting your friend should give you 5 feathers. There are some bonus feathers, IGN lists this bonus as 1 per friend, up to 5 total.

• Tapping on hearted heroes - 5 feathers

• Send Heroes Home - Note that I have found no sources that listed heroes to be worth more feathers based on level. Is it possible that your Tiki is 4 star?

• Completing Quests and Missions - Various Arena Quests are worth thousands of feathers

• Arena Rewards - Competing in an arena season can give you a large amount of feathers based upon your performance. You get separate rewards for offense, defense and overall rank.

• Special events - Nintendo may randomly run a special event which distributes feathers, such as the Global Retweet Event for 10,000 feathers

• Voting Gauntlet - There are occasionally Voting Gauntlets, which can also reward feathers. You 'vote' for your preferred hero and fight battles for them. You will receive 500 feathers any time your hero wins a round, in addition to rank based rewards.

• Hero Merit - A recent update added hero merit. You gain merit from battles, and when you accumulate 500 for a hero you receive 500 feathers. Other sources agree that you can get up to 2000 feathers per hero.

Sending Heroes Home

Arena Rank Rewards

Arena Offense Rewards

Arena Defense Rewards

Voting Gauntlet Round Rank Rewards

Voting Gauntlet Final Rank Rewards