It's nowhere near hopeless!

From those numbers, you're close to a great trip for two. The point of points is to take great trips without the big budget. It's tricky to find reports and bloggers in the middle. There are the "cheap" folks and the "snooty fancy pants" people. There aren't many quality middle reports now.

I'm going to assume you and your wife can schedule one joint week off. Maybe you could go this fall in October/November, or March/April 2014, giving you enough time to plan. Spring and fall are better times anyway - not too hot or cold. That gives you 9 days, counting the weekends. I would suggest this:
1) Fly to Seoul in business class on Asiana or United
2) Stay 3 nights at Park Hyatt Seoul
3) Fly to Hong Kong
4) Stay 3 nights at Hyatt Tsim Sha Tsui
5) Fly back to the USA.

This costs 240K United miles (transferring a few from Chase) and 90K Hyatt points (transferred from Chase). You don't even need a credit card application, though I'd consider the Hyatt card to get 2 free nights and free Internet. There are no visa costs for US citizens to Seoul and Hong Kong, and low airport taxes. There's plenty of good food for under $50 per person per day (less if you look around). Subway systems in both cities are good so transport is easy. Plus there are plenty of English speakers.

Thinking about my costs for those two cities, I think the two of you could spend about $1000 cash over those 9 days and have a wonderful time. Or you could substitute Tokyo for Seoul or Hong Kong. There are plenty of choices.