I agree that there are many different perspectives and aspects to be considered. I want to extend my opinion a little more on this subject.
Earthly hope is not something given to people by the holy spirit. You don't experience the certain moment that you realize you have earthly hope or feel the action of the holy spirit that gives you earthly hope. But you just like to be a human because you are a human. And after learning about paradise earth, you just want it. And we say we have an earthly hope because you want to live on a paradise earth. But you never know Jehovah really put us on a list of the paradise train or not. Of course, there can be help from the holy spirit for the earthly hope. But most of the people have no sign of holy spirit about their earthly hope.
For the heavenly hope, it is quite different. It is a natural thing for humans to desire to live on as a human. But for the people who were born again, it is like their minds and desires became already of spiritual beings even before they actually were resurrected as spiritual beings. They feel like they are captured into a fragile mortal body. They want to get out of the fleshly body. They want things in a spiritual realm which they don't know much about. For them, earthly things are not that interesting anymore.
2 Corinthians
"For we know that if our earthly house, this tent, should be torn down, we are to have a building from God, a house not made with hands, everlasting in the heavens. For in this house we do indeed groan, earnestly desiring to put on the one for us from heaven, so that when we do put it on, we will not be found naked. In fact, we who are in this tent groan, being weighed down, because we do not want to put this one off, but we want to put the other on, so that what is mortal may be swallowed up by life. Now the one who prepared us for this very thing is God, who gave us the spirit as a token of what is to come."
If someone was a JW before being anointed, that person may have been having earthly hope which means enjoying being a human and things on earth and hoping to go to a paradise on earth. But for those people who were anointed not knowing about paradise on earth, it would have not been like 'earthly hope changing to heavenly hope'. They already had a heavenly hope but after anointing, it got clearer. Actually, they didn't really have a heavenly hope before anointing. They were just wanting to get it. But being born again changes the deepest appetites and desires of the person. That is the real living hope. Clearly, the holy spirit changes the natural human mind into something unnatural for humans. This is an inner change from the deepest of your mind.
And about a million-dollar lottery ticket. Think about it this way. Once you accept the lottery, you have to leave your spouse or friends, the entire relationships you had as a human. And you should also abandon your body to become something very different being which you don't know very much. And even you have to leave not just an earth but the whole physical universe to live in somewhere you don't really know. Your whole life will change. In this case, there might be people who would give up the lottery. This is why some JWs think Jehovah should give them the right to accept or refuse. Because it is just too sad for them to leave everything behind. People have these kinds of questions don't understand the process of anointing. Your desire changes along with anointing. There is no way you can say you don't want it. It excels any human emotions. In this sense also, you don't have a choice.