I would like to use asymmetric encryption based with a private key based on a password. The requirement is the security level provided must be the same of (1) using password-bas
If you base the private key solely on a password, it will only be as strong as the password, i.e. whoever can guess the password can get the private key.
This is comparable to generating a private/public key pair, encrypting the private key with a symmetric cipher and then publishing both together.
This of course makes the whole system weaker, since you no longer need to have the secret token - you only need to know the password.