Economy availability is generally available on a widespread basis. You will have to call to get a comprehensive check of availability, as only a few options are available online. JAL isn't part of *A so you won't be able to use them to redeem your CO miles - are you sure you weren't doing a revenue search instead of a reward ticket search?

CO doesn't fly its own metal to SIN either - UA does, as well as SQ, TG, NH and several others that should offer decent connections. CLE-ORD-NRT-SIN, CLE-LAX-NRT-SIN, and several others may be worth looking at.

If you search in this forum you'll see many references to the ANA tool and the KVS and ExpertFlyer search engines - these can be very helpful for this type of search. The ANA tool on their website is free with some hoop-jumping (search for details).

I just did a quick search and saw several options in August routing through NRT. PM me if you'd like any specific help.