Hi there,

I'm thinking that the easiest way is to bring down the password protection with custom css, for example

form.post-password-form {
    margin-top: 25%;
}

in addition you can add specific margins for responsive, for example

@media only screen and (max-width: 768px) {

     form.post-password-form {
         margin-top: 60%;
     }

}

add the code to customizer -> additional CSS

the two css code snippets i ve sent you are dealing first with desktop and second with mobile