>> Many monergists, however, would counter that when the heart has been regenerated, man accepts God’s call freely and so would defend that their Christianity, while not predicated on freedom, did, in fact, involve their freedom. << — From Wikipedia
I hadn’t known this position to be consistent with Calvinism, but it certainly is consistent with Catholicism. (There are other statements, however, which suggest utter depravity, which is not compatible with Catholicism.**) Certainly, nothing you posted up through Martin Luther contradicts this understanding.
>> Opponents would argue that this type of freedom is akin to being free to take the one-and-only choice available. <<
Such opponents, I would say, misunderstand freedom. Freedom is NOT the ability to act capriciously. In fact, the person who acts capriciously is not acting based on any internal principle, and, therefore, in a sense, cannot be acting freely, merely chaotically. Freedom is the ability to act according to one’s own principles. If one’s principles are to act in a godly manner, than one is most free when he acts in a godly manner. So, Paul’s apparently contradictory notions of being a slave to Christ, while being liberated in Christ make sense: he is free to do what he desires to do, because what he desires to do is to be part of the body of Christ. When he could act capriciously in ignorance, he was not free, because he could not do what he ought.
"He said to them, 'But who do you say that I am?' Simon Peter replied, 'You are the Christ, the Son of the living God.' And Jesus answered him, 'Blessed are you, Simon Bar-Jonah! For flesh and blood has not revealed this to you, but my Father who is in heaven.'" - Matthew 16:15-17How could Peter have been utterly depraved when he said this? Yet if he were already saved, how could he deny Christ three times?
I don't know about Calvinism, but Catholicism states that Matthew 16:15-17 is an example of "prevening grace": Peter was not yet saved, yet grace could allow him to follow Christ, so that after the resurrection, he could be saved. (Peter's thrice denial of Christ was a mortal sin.) Certainly, the Holy Spirit did not move Peter to deny Christ, yet at the same time, certainly Peter was on the path towards salvation.
By recognizing sanctification as a process, not an instantaneous event, the Catholic Church is able to hold simultaneously that grace cannot be thwarted, yet people can choose to sin even while grace is at work within them.