I would open up the alpha only if you have third parties (or customers) who want to write to your API. Then you should get it into their hands as soon as possib

I would open up the alpha only if you have third parties (or customers) who want to write to your API. Then you should get it into their hands as soon as possible. Otherwise, wait until you have a solid beta. If you screw up your first release (whether, alpha OR beta) you may not recover. Better to make them wait. After your first solid release, you can go agile-style incremental.