Citibank Singapore might do it, into a U.S. dollar account. Their pricing guide suggests it's possible. That's a fairly chunky amount of cash, though, which will probably give them pause. (Good grief.)
If it is possible deposit that stuff into Citibank, then Citibank Global Transfer lets you move it to another Citibank account in the U.S., if you have one, free of charge. Thence into something that could generate some interest. (And for spending down using a low cost U.S. debit or credit card.)
Personally, I'd just save the stuff to spend when I'm on my next trip somewhere that likes U.S. dollars: the United States, Ecuador, East Timor, El Salvador, the Marshall Islands, Micronesia, Palau, Turks and Caicos, the British Virgin Islands, or Zimbabwe. There are also several countries that peg their currencies to the U.S. dollar, so a straight/steady currency swap should be possible. A lot of those countries are in the Middle East, such as Bahrain, Saudi Arabia, the UAE, Lebanon, Qatar, and Oman. Hong Kong pegs within a narrow band to the U.S. dollar.
Please note that you'll have cash declaration report(s) to make if you try to carry all or most of that cash across a border. The U.S., for example, requires a declaration if you're carrying US$10,000 or more total in cash and cash equivalents. Singapore requires the same starting from S$20,000 worth of cash and cash equivalents, so you've got a Singapore cash declaration to make also if you're carrying that cash out of Singapore.