hi Oynnet, glad you found the forum.
As fini said, your boundaries are all about you, so when you mentioned feeling resentment toward him for "crossing that boundary" it perhaps means that you aren't really clear on boundaries? What you've given him is a rule, not a boundary. So for instance, a rule would be:
Don't ever ask me for any financial support or try to make me feel guilty about not financially supporting you.
A boundary would be:
I will not financially support anyone except myself and my non-adult children.
See the difference there? With a rule, you are asking someone else to follow your rule. They don't have to, they don't even have to listen to it. There is no real repercussion for not following it and really, rules are only for kids.
With the boundary, that is totally within your control, the other person doesn't have to do a single thing and they don't get a say in your boundary. It's yours. You are the only person you can control, so that works well.
He is struggling with wanting to quit drinking in my opinion. He may well love you very much, as much as he is capable of while being in active addiction. You really don't want to be his anchor do you? He may well feel better (for now) when he is with you, but that's a change of scenery, you taking care of everything etc. He'll quit drinking when he is ready, not just because he's feeling better about being somewhere else. It's a false illusion. I'm sure he wants to believe it, but is it true? If love and care could cure alcoholism - well you get the drift.
He is taking advantage. I'm sure he says he would do the same for you! Well he might, if he had a better paying job. Is unemployment high there, is there any reason he can't get a better paying job?
As an aside, I assume he doesn't have U.S. citizenship, so it could take up to a year even for him to get a K1 visa to come to the U.S. and even then he won't be able to even look for a job for several months. You could be setting yourself up here. Has he ever had a DUI?
If he's serious about all this, are there zero places for alcoholism treatment in Australia that he could attend? If he's serious wouldn't he at least try AA? Or Smart Recovery or some support, anything, his GP.
Anyway I think he's pondering moving where he will be forced to quit or not. He may say he wants to quit but perhaps ask him does he want to quit or does he really just want to want to quit.