IDK, why don't you go ahead and answer that question? Either way, you're still not addressing the question. Should a believer persistently engaging in grave ugly sin expect to enter heaven? And will that believer nonetheless engage in lighter sins?
Are we talking about unrepentant serial killers? I suppose that God could have mercy on them if they turned to Christ. Jesus said every sin except "blasphemy against the Spirit" can be forgiven (Mt 12:31).
9 Also He spoke this parable to some who trusted in themselves that they were righteous, and despised others: 10 “Two men went up to the temple to pray, one a Pharisee and the other a tax collector. 11 The Pharisee stood and prayed thus with himself, ‘God, I thank You that I am not like other men—extortioners, unjust, adulterers, or even as this tax collector. 12 I fast twice a week; I give tithes of all that I possess.’ 13 And the tax collector, standing afar off, would not so much as raise his eyes to heaven, but beat his breast, saying, ‘God, be merciful to me a sinner!’ 14 I tell you, this man went down to his house justified rather than the other; for everyone who exalts himself will be humbled, and he who humbles himself will be exalted.” (Lk 18:9–14)
This reminds me of a kind of relativistic righteousness -- thinking we are right with God because our sins are smaller, less ugly, and more infrequent than other people's sins. It's only when we admit that we are sinners in desperate need of God's forgiveness that we don't point our fingers at other people and say, "Thank You that I'm not like these extortioners and adulterers".
The fact is, all our sins count against us. Without Jesus sacrificing Himself for all our sins, none of us could be saved. And we're not saved because we are good partners with God. We are saved because Jesus loved us enough to pay the price for all our sins.
And there is a reason sin-avoidance is not an effective strategy for maintaining eternal life. You like to quote Romans 2:13 -- "for not the hearers of the law are just in the sight of God, but the doers of the law will be justified" (Ro 2:13). But you don't put it with the conclusion of the topic:
For we have previously charged both Jews and Greeks that they are all under sin.
10 As it is written:
“There is none righteous, no, not one;
11 There is none who understands;
There is none who seeks after God.
12 They have all turned aside;
They have together become unprofitable;
There is none who does good, no, not one.”
13 “Their throat is an open tomb;
With their tongues they have practiced deceit”;
“The poison of asps is under their lips”;
14 “Whose mouth is full of cursing and bitterness.”
15 “Their feet are swift to shed blood;
16 Destruction and misery are in their ways;
17 And the way of peace they have not known.”
18 “There is no fear of God before their eyes.”
19 Now we know that whatever the law says, it says to those who are under the law, that every mouth may be stopped, and all the world may become guilty before God. 20 Therefore by the deeds of the law no flesh will be justified in His sight, for by the law is the knowledge of sin. (Ro 3:9–20)
It is not possible for sin-avoidance to make a person right with God because "all have sinned and fall short of the glory of God" (Ro 3:23). This is the best place to keep one's mind.