Hi
A guys view on this. I know many of you ladies can offer really good advice with difficult stuff like this, so I'll try my best!
Anyone who wakes up wanting a drink, is an alcoholic. At that level of physical dependency, there does as already been said, need to be a drastic change in order to come to terms/deal with/ reduce and remove the dependency. It sounds as though he is a nice person from what you've described when he does talk nicely with you. However it seems to go out the window once the alcohol flows. It's a very very weak argument to say 'it's the british culture' and that's why he drinks to the levels he does. That is nothing short of a copout.
I know it' easy to say from an outsider's point of view, but I'd say perhaps give him 3 or 6 months to change his ways or at least seriously attempt to change his drinking/alcoholism in order for you to keep considering a relationship with him. I know that might cause arguments or tension, but surely, it'd be worth it to see how he reacts to it all and that will in turn help you evaluate if it is indeed worthwhile for you to pour energy into this relationship. You've got to the level of discussing marriage which makes it a little more problematic. Reading between the lines, if he's not able to travel to or within the US, it suggests things he's done/involved with in the past which is relatively serious.
You do have some thinking to do for sure.
Just to give you an example of something similar - a very good friend of mine, she was just 2.5 weeks away from her wedding to a guy - and in Indian circles/weddings that isn't just cutting it fine, it's REALLY cutting it fine.. She called it off and when I heard why, myself and all her friends gathered to support her. It took her well over 3 years to finally move on and she's now very happily married - I distinctly remember her words "but I was so sure he'd change after I married him" - I and the rest of us are really glad she 'woke up' in time. I'm not saying its the same as your situation, however it is very close.
Good luck with whichever way you go eventually go!
Cheers! DtM! West London & Slough UK!