Monergism/Synergism is a false issue.
Faith is not a work and thus cannot be viewed as adding anything to salvation.
The real issue is which comes first regeneration or faith, and the Bible says Faith.
As for keeping 'busy' after, what are you doing during your Christian walk.
Are you cooperating with God?
Is God controlling your every thought or are you resisting God when you refuse to yield?
Are you obeying God when you do yield?
Your progressive sanctification smacks of synergism (since you regard faith as a work)
The only alternative is that you are sinning because God will's that you sin and Rom.6:16-18 is just one of those 'facade' verses that is hiding the 'secret will' of God (as Calvin explained 2Pet.3:9 to be, and Spurgeon and Piper explained 1Tim.2:4 to be)
That's not what Paul says.
"We give thanks to God always for you all, making mention of you in our prayers; Remembering without ceasing your work of faith, and labour of love, and patience of hope in our Lord Jesus Christ, in the sight of God and our Father; Knowing, brethren beloved, your election of God. For our gospel came not unto you in word only, but also in power, and in the Holy Ghost, and in much assurance; as ye know what manner of men we were among you for your sake." -- 1 Thessalonians 1:2-5