Are you mostly saved by grace but still have to work to keep your salvation?

After all, if Noah (and his sons) did not build the Ark, they would have drowned like the rest of the world.

That is true. Jesus Himself said that those who love Him obey His commandments (John 14:15).

So, does obedience of the commandments of God save us?

Nope. Scripture is clear. No ritual or work can save us. Only God does.

Noah, then, would have to have been saved spiritually before he built the Ark (2 Corinthians 2:15) since we know that salvation and faith are both gifts from God (Ephesians 2:8-9) and no unsaved person can obey God in the fullest sense (Ephesians 2:2-3).

His building of the Ark, therefore, is a manifestation of the salvation already there. Because he loved God, he obeyed God.

I had a youth pastor who used this illustration; blood doesn't force the heart to pump by flowing through it. The heart pumps the blood by itself, giving the body life.

The illustration isn't perfect, but the idea is what is seen: our work is a natural effect of the cause, salvation.

It’s not as though God was doing things differently in the Old Testament than He did things in the New Testament. God is the same always (Hebrews 13:8). This doesn’t mean we therefore adopt the works-based religion of the religious leaders that Jesus condemned. This means we apply God’s truth consistently.

Am I saying that Christians never sin after they're saved?

No, but I am saying that Christians obey the commandments of their king because their king has saved them. If you trust that you can do enough good things to counter-balance your bad things, then you don't have Christian salvation.

Luckily for you, salvation is a free gift to those who desire it.