I believe largely as you do. I simply believe your presentation mutes your message.
Don't believe me; rather believe the Holy Word of God. The bottom line here to this "men seeking God" issue is that scripture basically says two things about this: The natural man [left to his own evil devices] does not seek after God (Rom 3:11). On the other hand, those who do seek God and his Christ do so entirely by God's grace (Jn 6:65) -- not by their natural ability or inclination or desires or the mighty power of their "autonomous free will".
If evil men
cannot say anything good because the mouth
can only speak by that which overflows the heart (Mat 12:34-35); or if, conversely,
no one speaking by the Spirit of God
can say, "Jesus be cursed", and
no one can even say from his heart that "Jesus is Lord" either, except by speaking from the same Spirit (1Cor 12:3), then how much less can unregenerate, God hating, sworn enemies of God and rebels from birth (Ps 51:5; Job 25:4-6; Isa 48:8) change their hearts to have godly desires that would incline them to seek after the Lord God?
The devil has planted many tares (his sons and daughters) in Christ's Church, so verify everything by the inspired, infallible, authoritative Word of God. " Let God be true and every man a liar" (Rom 3:4)!