You have it totally wrong.
The offer of eternal salvation is not a "carrot and stick" scenario.
Yet the rest of your answer exactly describes a carrot and stick scenario. Are you so blinded by your faith that you can't see that? As for "
...loving the Lord your God with all your mind, heart and strength.", that is a vile, narcissistic demand.
And that's not to mention the silly and cruel game of hide-and-seek that your god (if it exists) is playing for people to even accept its existence, let alone carrot and stick choice you then have to make if you do accept its existence and message.
And all that then leads us to the basic problem with the concept of 'free will' that have been much discussed already.
Absurdity piled on top of absurdity. It would be hilarious if so many people weren't taken in by it.