Yep...Newton's letters were instrumental in helping me out of quite a depression over Sanctification. I remember always being impressed by Newton's perspective, with prayers like, "Lord, please direct our hearts towards your ways." He acknowledged God as the primary mover in all things, including Sanctification. He recognized his dependence upon God's hand in each matter. God could direct him through seasons of triumph or failure, and each would accomplish the desired effect. It served to strengthen his dependence upon God, and his trust in the gospel, as his internal focus was forced to look outward to his grace alone, because that was all that was left. It allows one to be honest about his true internal condition, and feel relief over its forgiveness. And that forgiveness becomes quite motivating to want to follow God's ways. I remember finally being able to tell God that I loved him, and knowing that I really meant it.
From the same letter you quoted:
"...If the evils we feel were not capable of being over-ruled for good, he would not permit them to remain in us...As to the remedy, neither our state nor his honour are affected by the workings of indwelling sin, in the hearts of those whom he has taught to wrestle, strive, and mourn, on account of what they feel. Though sin wars, it shall not reign; and though it breaks our peace, it cannot separate from his love. Nor is it inconsistent with his holiness and perfection, to manifest his favour to such poor defiled creatures, or to admit them to communion with himself; for they are not considered in themselves, but as one with Jesus, to whom they have fled for refuge, and by whom they live a life of faith. They are accepted in the Beloved, they have an Advocate with the Father, who once made an atonement for their sins, and ever lives to make intercession for their persons. Though they cannot fulfill the law, he has fulfilled it for them; though the obedience of the members is defiled and imperfect, the obedience of the Head is spotless and complete; and though there is much evil in them, there is something good, the fruit of his own gracious Spirit...They shall not always be as they are now; yet in a little while, and they shall be freed from this vile body, which, like a leprous house, is incurably contaminated, and must be entirely taken down. Then they shall see Jesus as he is, and be like him, and with him for ever."
"...If a mariner is surprised by a storm, and after one night spent in jeopardy, is presently brought safe into port; though he may rejoice in his deliverance, it will not affect him so sensibly, as if, after being tempest-tossed for a long season, and experiencing a great number and variety of hair-breadth escapes, he at last gains the desired haven. The righteous are said to be scarcely saved, not with respect to the certainty of the event, for the purpose of God in their favour cannot be disappointed, but in respect of their own apprehensions, and the great difficulties they are brought through. But when, after a long experience of their own deceitful hearts, after repeated proofs of their weakness, wilfulness, ingratitude, and insensibility, they find that none of these things can separate them from the love of God in Christ, Jesus becomes more and more precious to their souls. They love much, because much has been forgiven them. They dare not, they will not ascribe anything to themselves, but are glad to acknowledge, that they must have perished (if possible) a thousand times over, if Jesus had not been their Saviour, their shepherd, and their shield. When they were wandering he brought them back, when fallen he raised them, when wounded he healed them, when fainting he revived them. By him out of weakness they have been made strong; he has taught their hands for war, and covered their heads in the day of battle. In a word, some of the clearest proofs they have had of his excellence, have been occasioned by the mortifying proofs they have had of their own vileness. They would not have known so much of them, if they had not known so much of themselves."
"...A broken and contrite spirit is pleasing to the Lord who has promised to dwell with those who have it; and experience shows, that the exercise of all our graces is in proportion to the humbling sense we have of the depravity of our nature. But that we are so totally depraved, is a truth which no one ever truly learned by being only told it. Indeed if we could receive, and habitually maintain, a right judgment of ourselves, by what is plainly declared in Scripture, it would probably save us many a mournful hour; but experience is the Lord's school, and they who are taught by him usually learn, that they have no wisdom by the mistakes they make, and that they have no strength by the slips and falls they meet with. Every day draws forth some new corruption which before was little observed, or at least discovers it in a stronger light than before. Thus by degrees they are weaned from leaning to any supposed wisdom, power, or goodness in themselves; they feel the truth of our Lord's words, 'Without me ye can do nothing;' and the necessity of crying with David, 'O lead me and guide me for thy name's sake.' It is chiefly by this frame of mind that one Christian is differenced from another; for, though it is an inward feeling, it has very observable outward effects, which are expressively intimated, Ezek. 16:63, 'Thou shalt be dumb and not open thy mouth, in the day when I am pacified towards thee, saith the Lord God.' The knowledge of my full and free forgiveness of thy innumerable backslidings and transgressions shall make thee ashamed, and silence the unruly workings of thine heart. Thou shalt open thy mouth in praise; but thou shalt no more boast in thyself, or censure others, or repine at my dispensations. In these respects we are exceedingly prone to speak unadvisedly with our lips. But a sense of great unworthiness and much forgiveness checks these evils. Whoever is truly humbled will not be easily angry, will not be positive and rash, will be compassionate and tender to the infirmities of his fellow-sinners, knowing, that if there be a difference, it is grace that has made it, and that he has the seeds of every evil in his own heart; and, under all trials and afflictions, he will look to the hand of the Lord, and lay his mouth in the dust, acknowledging that he suffers much less than his iniquities have deserved. These are some of the advantages and good fruits which the Lord enables us to obtain from that bitter root, indwelling sin."
Blessings!