You could whitelist the email providers, and require "strange" email providers to be approved by mods. The workflow would look like this:

1. Sign up with Gmail 2. Verify email 3. Account is instantly approved

1. Sign up with sharklasers 2. Verify email 3. "You're using a weird email provider. Mods will look at your account and see if it looks OK. If so, we'll approve it"