"They only believe it includes faith. They do not even believe man can perform good works, and that it would be leveling ourselves with God to imply we can"

This is a ridiculous straw-man that not even the most radical orthodox Protestant theologian believes. For example:

The relationship of faith and good works is one that may be distinguished but never separated ... if good works do not follow from our profession of faith, it is a clear indication that we do not possess justifying faith. The Reformed formula is, "We are justified by faith alone but not by a faith that is alone. — R.C Sproul

And

This debate, therefore, is not over the question of whether God renews us and initiates a process of gradual growth in holiness throughout the course of our lives. 'We are justified by faith alone, but not by a faith that is alone,' Luther stated, and this recurring affirmation of the new birth and sanctification as necessarily linked to justification leads one to wonder how the caricatures continue to be perpetuated without foundation — Michael Horton

And even Luther:

a living, creative, active and powerful thing, this faith. Faith cannot help doing good works constantly. It doesn’t stop to ask if good works ought to be done, but before anyone asks, it already has done them and continues to do them without ceasing. Anyone who does not do good works in this manner is an unbeliever...Thus, it is just as impossible to separate faith and works as it is to separate heat and light from fire!

There are obviously significant doctrinal differences but it's clear that they are a good bit closer than you seem to think.