in your case the first prompt is actually for password. But it does not mean that it must work it this way generally.
In most systems you know what the first question will be. It might be a password or time dependent id. In those systems user doesn't need to see the prompt and will (without thinking) type the "password" to first possible location.
More complex systems might have for example 20 different questions from witch one is selected by random and asked from the user. The questions have user selected answers. This type of system needs user to recognice witch "password" to use in order to log in. That is why I suggested only sending the password text to keyboard interactive system if it is non-empty. These are cases where you have to wait for the prompt to appear to make a decent selection.
What I can do it to add button "use password" on the prompt. Which would reply to server with password stored in the session (if any). Is it OK?
As long as it applies only to the first prompt (and is a default setting) I would be very happy.
I'll setup a test account tomorrow and inform you outside this forum.