I was in this same situation for our 10th anniversary when we went to the Polynesian. I could not justify the cost of having it delivered and could not find anyone to give me a better idea. Here is what I did: I bought a bottle of champagne at home and packed it in my suitcase (bubblewrapped, in a plastic bag that I sealed shut with tape). Then, I also tucked in glasses, some chocolates, and a bucket. Yes, it was a pain in the neck to get this all in my suitcase but I kept on thinking of how special it would be and how it was really my only option because of the money. When we got to the Polynesian, I waited until my husband took his shower. I quickly got ice and set everything up. When he came out, there was the surprise. It would have been neater if it was actually waiting in our room when we got there or on a day when we got back from the park - but - to be honest, my husband would not have cared either way. Instead, he knew how hard I had to work to get it all there and set it up for him. We let it sit all day in the room on ice and then came back to our room at night for a romantic treat. Knowing about it all day was also good - I think we had a special day together knowing that we were going back for a romantic treat. We actually took our drinks and chocolates out to watch the fireworks together. Thinking of how romantic that was makes me think I may try this again this year when we go back!
Good luck!