The Early Reformers Did speak plainly and understood what Jesus said on this. We have done poorly- if at all- contextuallizing this understanding.
Your quotes on Rms are dead on. “The Wages of sins is death” Rms 6 was written to Believers-
There is to be lifelong putting off of sin and a putting on of Christs ways- Righteousness. This is connected to Promises in Baptism- God to us and us to God.

Rms doesn’t stop at Rms 7- it continues as a unit on to Chapter 8- again your context is correct. These are connected units of thought from God.
Back to Jesus and the undertanding- of “Mortify the flesh”.
Matt 5 27 “You have heard that it was said, ‘Do not commit adultery.’ a 28 But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart. 29 If your right eye causes you to sin, gouge it out and throw it away. It is better for you to lose one part of your body than for your whole body to be thrown into hell. 30 And if your right hand causes you to sin, cut it off and throw it away. It is better for you to lose one part of your body than for your whole body to go into hell.

Note also- Jesus says this again later in Matt 18.

7 “Woe to the world because of the things that cause people to sin! Such things must come, but woe to the man through whom they come! 8 If your hand or your foot causes you to sin cut it off and throw it away. It is better for you to enter life maimed or crippled than to have two hands or two feet and be thrown into eternal fire. 9 And if your eye causes you to sin, gouge it out and throw it away. It is better for you to enter life with one eye than to have two eyes and be thrown into the fire of hell.

This is in the context of Church discipline for public unrepentant sin. Why?

I will roughly quote from Walthers Pastoral Theology:
#1 So the person caught up in sin may know how serious God takes sin and Repent.
#2 So the Repentant Sinner may be lovingly restored to the Kingdom of Grace and loving embraced by all in the Congregation
#3 So that the Watchers may take Warning on the seriousness of sin.

End

The Critical point is the Attitude of our Hearts towards our sins.

Have you ever read “The Hammer of God”? It is required at the Sems. It is a quality work. I need to re-read it.

From the Hammer of God pg 66.

The next question came from the housewife in who’s home they were guests. “How great shall our sorrow over our sins be if it is to be sincere?”

So great that one is willing to give up the sin,” answered Linder promptly. “Crocodile tears mean nothing in heaven. But he who wants to be free from the sin has true sorrow even though the heart feels hard as a stick.”

“What Luther Says” by Pless pg 738 :-
Nonetheless man must hear the Law first, then the Gospel.

Before receiving the comfort of the forgiveness, sin must be recognized and the fear of Gods Wrath must be experienced through the preaching or apprehension of the Law, that man may be driven to sigh for Grace and may be prepared to receive the comfort of the Gospel. There fore one should by all means most severely admonish and drive to repentance with threats and intimidation those who are yet without and fear of God’s wrath, are secure, hard and unbroken. That is, no Gospel but only Law and Moses should be preached to them.
On the other hand, where there are hearts in which the Law has performed it’s Office, so that they are frightened by the knowledge of their sin, are timid and fugitive, no Law should be preached and proclaimed any more, but the pure Gospel and comfort. For this is the proper Office of Christ, to perform which He came and commanded the Gospel to be Preached to all poor sinners and enjoined on them to believe it, that He might abolish and remove all charges, frightenings and threatenings of the Law and might give them the purest comfort instead.
End

This has been forgotten in todays churches. -DR