Well, in this case (having gone back and actually checked the docs rather than relying on recollection roughly a decade old) you could store MD5(username:realm:password) rather than password, though that doesn't buy you all that much in a case like this where making the password a long, random string that's not reused is not only good practice but also easy and so likely to be general practice.
Stipulating all the other points you've made, exactly what is the purpose of hiding from a server a long random string generated by that server and useful only to that server?
If you have the hash, you can log into the site (just not using the typical libraries), so it really doesn't add a lot of security. That's why I was wrong :-P
