You know that Rom.6:16 is referring to the choice that a saved man makes to either stay in the Spirit or in the Flesh?
So the regenerate man does make choices between God and the Flesh by 'yielding' to either one or the other (two natures).
If this were not the case then you are left with a saved man either not sinning again or God being responsible for his sinning.
This is the view that that L.S. Chafer taught.
(I know,I know he wasn't a real Calvinist!) :>)
As for saving grace, if God initiates and reveals Himself, why cannot man freely either respond or reject the light shown to him. (Jn.3)
Regeneration does not precede faith but is the result of it and faith is what man must do both to be saved (accept the gift) and in growing up (yielding)
We walk by faith, not by sight.(2Cor.5:7)
The Jews that did not enter the land did not do so because they did not mix the promises of God with their faith (Heb.4:2)
Now you know we disagree :)
Hope you are well and blessed in this new year !