Mark,
You said:

Let me see if I understand your view.
1. Jesus draws every single person in the world to himself
2. But not everyone comes to the Father
3. Those who come to the Father are those who are seeking/fear God and therefore believe.

3 is not right. Although all those who fear God will be brought to the covenant, God still calls those who don’t fear God and they can obey God when He calls them.

I have a problem with this. Even in my own experience this doesn’t work.

You probably should have checked first before find a problem with your misunderstanding.

God doesn’t reward those who are seeking him more than those who are not.

Malachi 3:16–18 (NASB)
The Book of Remembrance
16 Then those who feared the LORD spoke to one another, and the LORD gave attention and heard it, and a book of remembrance was written before Him for those who fear the LORD and who esteem His name.
17 “They will be Mine,” says the LORD of hosts, “on the day that I prepare My own possession, and I will spare them as a man spares his own son who serves him.”
18 So you will again distinguish between the righteous and the wicked, between one who serves God and one who does not serve Him.

Mark, it looks like you are contradicting God who rewards those who fear Him by making a difference between the righteous (those who choose to fear God) and the wicked who refuse to fear God. I choose to believe God.

This view gives us room to boast. I got salvation because I was seeking type of idea.

No room to boast since we cannot earn salvation. Those who fear God are not the ones who are boasting, but they are humbled by their recognition of their need for God.

We are saved purely by the mercy and grace of God. But maybe this isn’t how you see it/ Let me know

We are not saved by fear, but God promises to bring those who fear Him to salvation. It is purely by God’s grace. Read the passage above again and see what you think. What is God saying? Is God lying to us or does He really make a difference between those who fear Him and those who do not.