In addition to the IP, to prevent abuse just have more captchas.  Solve one captcha for the first claim, two for the second claim...five for the fifth claim.

An alternative, you can present the user with 10 captchas, 5 of which are real and 5 are which are from a "solve a captchas" bitcoin paying service. 

5 captchas solved are worth about 3 bits and should provide a nice way for users to fund the faucet for you.