1. DL has offered you some valid options including a refund. At this point, that might be your best route versus trying to deal with rerouting.
2. Did you book the flight seperately? If you did, it is up to you to fix it to get on the cruise. (If you booked it with your cruise, then it is the travel agent's/cruise company's responsibility to get on the boat). DL isnt responsible for any hotel rooms as the have given you options well in advance of your travel.
3. American Arilines is NOT a partner with Delta and therefore there is very little DL could do to place you on a competitor's airline.
4. If you wanted to fly on a partner, you should be prepared to give DL some valid flight option on Skyteam partners (www.SkyTeam.com)
5. It is your honeymoon, congratulations. If none of the options work out, take the refund and find somewhere else to go. It is much easier to deal with than fighting with DL (or any other airline) at this point.
6. If you can find other flights (on airlines not AA) with a stay the night before, book it and suck up the hotel charge. If you're so strapped for cash that you can't afford another night in Quito (the 5-star JW Marriott is $200, the 4-star Swissotel is $175), would it be better to find a cheaper honemoon. DL has provided you with that idea and that option where a full refund might be provided.
7. On schedule changes like this, DL ends to be quite flexible with rebooking(within reason). You should arm yourself with valid options (other flights on other partner airlines). DL isn't going to pay for hotel rooms or other trvel related changes. As I've said, refund is a valid option.

Welcome to FT.