I really appreciate the heart behind this. God's grace is truly greater than our sin, and Scripture absolutely gives hope to the repentant sinner. We should run toward Christ rather than away from Him when we fall.
That said, I think there are a few places where we should be careful not to say more than Scripture says.

First, Scripture teaches that all sin makes us guilty before God and that every one of us needs the cross. But I don't think Scripture teaches that every sin is identical in seriousness or consequence. Jesus Himself spoke of “greater sin” (John 19:11), so saying that God doesn't “categorize” sin seems too absolute.

Second, I would be careful with the statement that every individual sin temporarily separates a Christian from God until that particular sin is confessed. Sin certainly damages fellowship with God and needs to be dealt with, but 1 John 1:7 says that “the blood of Jesus his Son cleanses us from all sin” as we walk in the light. Our relationship with God rests ultimately on Christ's finished work, not on our ability to remember and confess every individual failure perfectly.

Third, Hebrews 8:12 saying that God will “remember their sins no more” doesn't mean God literally forgets that they happened. It means that He no longer holds forgiven sin against His people. God's forgiveness is not divine amnesia; it is divine mercy.

I'd also be cautious about saying that a particular sin necessarily means we've lost a particular heavenly reward. 1 Corinthians 3:15 does speak about suffering loss while still being saved, but the immediate context concerns the testing of a person's work. The passage doesn't give us a formula by which we can say, “I committed this sin, therefore I lost this reward.”

And perhaps most importantly, we shouldn't automatically label all painful guilt after sin as Satan's accusation. There is such a thing as false condemnation, but Scripture also speaks of godly sorrow that produces repentance (2 Corinthians 7:10). Conviction can actually be God's mercy because it brings us back to Him.

So I completely agree with the central encouragement: don't run from Jesus when you sin. Run to Him. But I think grace should make us neither presumptuous nor despairing. Grace doesn't mean sin doesn't matter. It means that when we truly repent, we don't have to hide from the One who already knows our sin and offers mercy through Christ.

Hebrews 10 itself holds both truths together: it gives a serious warning about deliberate, persistent rebellion, while the surrounding passage calls believers to draw near to God with confidence because of Christ's sacrifice.

The gospel isn't “You sinned, so you're finished.”

Nor is it “You sinned, but it doesn't really matter because grace covers it.”

It is: Christ has paid for sin, therefore repent, receive His mercy, and keep following Him.

That's a much bigger picture of grace.