I am not familiar with Edwards' work, but for seventeenth-century Puritans your best source is Anthony Burgess, "A Treatise of Original Sin," (London, 1658). The best general summary of Puritan thinking on sin and its psychology is Richard Bernard's popular "The Legal Proceedings in Man-Shire Against Sinne."
When studying Puritan thinking about sin, watch out for the difference between sinning in the outward, observable, physical behavior and sinning in the inner world of thoughts, fantasies, desires and emotions -- the rules that dealt with this later obedience were usually denoted by the expression "spiritual law." Puritans required both types of obedience, but they held the inner, "spiritual" obedience to be more important:
" . . . keep [religion's] law spiritually, because it is spiritual . . . indeed in this it does especially differ from the laws of men: for they do tie the hand, and the tongue, and the foot, to the good-abearing, and take note if any of these are faulty against them; but they meddle not with the heart, and make no question of the inward motions of the soul . . . But God searches the hearts and tries the reins, and enters into the secrets of the soul: and therefore he commands to love him with all our heart, and with all our soul; not contented with such a love only, as is declared by the outward behavior of the body . . . all the obedience performed to God must proceed from within, and come from the heart, else it shall be no whit acceptable to him." (John Dod & Robert Cleaver, "A Plaine and familiar Exposition of the Ten Commandements," (London, 1604), 8.)
In practise the "spiritual interpretation" of law meant that truly religious people not only had to behave virtuously, they had to feel that behavior as pleasant. Similarly, people who had been touched by grace did not just leave sins undone, they felt them as disgusting. The requirement to obey in emotions explains the "law demands the impossible" idea, that was central to Protestantism. After all, people cannot control their emotions by willpower.
The significance of the difference between external and internal obedience is highlighted by the hypocrisy concept: hypocrites often performed the outward obedience better than truly religious people, but they failed in the "spiritual obedience" of thoughts and emotions.
The division between inner and outward obedience is easy to overlook, because the two types were usually discussed separately. For example, the most popular Puritan writer before 1640, William Perkins, discussed the outward obedience in his "Cases of Conscience" and the inner obedience in his "A Treatise of Man's Imaginations." The tone of the latter book is summed on pp. 98-99: "the second Table of the morall lawe, which was penned with respect to the corrupt estate of man, forbidding that which man's corrupt heart thinks naturally against his neighbour: for every commandement thereof is spiritual, forbidding not only the wicked actions, evil words, and gestures, but all corrupt affections, yea all evil Imaginations of man against man."