In light of this, how can we understand the B'racha of Hashiveinu in Shemoneh Esrei, in which we ask God to bring us closer to Him and to bring us to repent completely? Doesn't this run contrary to the idea of free will?
The Migdol Dovid writes that we are davening that Hashem remove the practical obstacles to doing teshuva - once we have the intellectual desire to do teshuva, Hashem can assist us to actualize our intellectual decision. This is not unlike the idea of הבא ליטהר מסייעין אותו (Yoma 38b) - one who comes to purify himself receives [divine] assistance.
Rabbeinu Yehuda Ben Yakar understands this to be the meaning of החזירנו בתשובה שלימה לפנך - bring us to complete repentence before you - we cannot ask Hashem to initiate the teshuva process - tefillah only works after teshuva, as הכל בידי שמים חוץ מיראת שמים. We only ask for the completion of the teshuva process to be assisted from above.