Finally, there is a solution. LastPass Plus gives the ability to input usernames and passwords into apps. It does this by using a custom keyboard. Is it a perfect solution? No. Does it work? Yes. The keyboard itself is not nearly as good as the stock Android keyboard so its annoying to use for other apps, but what I do is use it only for the time that I need it and then switch back to stock when I don't. Once again its not perfect, but it works. I don't see another way to do it with the present state of Android. The only other way to do it would be with Intents, but I'm pretty sure Intents don't provide the security needed to be requesting and sending passwords back and forth.
Until Android gets serious about password management, LastPass has a working solution. I am very pleased that this solution is available to me as it solves a nagging problem.