How can the worship of supplication be reconciled with God's sunnah of granting humans free will without nullifying either of them?

There is no contradiction between the worship of supplication (du'a') and Allah's cosmic laws. Supplication is a means to achieve what is destined, just as eating and drinking are means to attain satiety and quench thirst. Legitimate supplication is that which involves no transgression. Transgression in supplication occurs when one asks for something impermissible, such as seeking assistance for forbidden acts, or asking for something Allah does not do, such as requesting immortality or infallibility. Supplication that seeks to suspend cosmic laws is considered an act of transgression and will not alter Allah's established laws, which do not change or transform.