I agree I would take it to the highest level - past this manager. That's the first thing I would do. There is always the local press as well.
Sure, you don't have a written contract - but I'm sure they don't want people to know about what their word is apparently worth.
"I'm so upset right now, and you don't seem to be doing anything... since you are 'technically correct' and I don't have it in writing I don't think it is worth taking it to the BBB. I would have thought our long-standing relationship and the clients I've sent to you over the years would be worth something." "If the only option I have left is taking it to the press, I will."
Since it is the location vs the amount of people there and it is more important to the B&G to have the location, I would just go with that. Cut your numbers and have your bar or limited bar. It's hard to go forward with a light heart if you can't fix this, to be treated so disdainfully, but if these are your options and they are determined to stay, then work within the budget and go for it. Then sigh, and enjoy the rest of the planning and wedding.
Although I do agree it would be kinda tacky to have a cash bar once people were travelling, I would let the B&G make that call, if they want a cash bar, go for it. REALLY WHO CARES???? Just let the guests know beforehand.
Myself, I am not offended by a cash bar, even if I travel, I am there because I LOVE the couple and want to share in their happiness. Not because I'm getting anything free... I would send a gift whether there or not and enjoy the trip were I to go. I don't need to feel paid or entertained to want to go.
And I do hope alcohal is available for purchase somewhere on site if you don't have a cash bar in the room... I still like my glass of wine.
I would definitely have wine on the table at the very least.
Good luck, keep trying with the resort and in the end just follow the couple's wishes within the budget... they might be willing to pitch in. I paid for pretty much my entire wedding. My parents chipped in, but mostly it was DH and myself. I didn't mind. In fact anything they wanted to help with was enough.