In cities where the Asian immigrant population is significant, there are Asian-operated travel agencies that specialise in Asian travel. The prices they offer are usually very competitive. Here's one (based in NYC) I used to call and have them mail my tickets to me when I lived in upstate NY: L&Y Travel Services Co. (Multi Service Enterprises, Inc.) tel:
I left the states 6 years ago, so it may not exist anymore or may operate under a different name etc. If you know anyone of Asian origin who travels fairly often to Asia, ask him/her to recommend a travel agency. Obviously, there are bogus ones out there, so you should be extra careful (e.g. keep receipts, faxes etc.) and ideally go to one that has been recommended to you by someone you trust. Pls note that I do not, in any way, guarantee the service of L&Y. You might just want to call up and get some quotes. After that, you can compare prices with those that your local travel agent or known online budget travel sites will offer. My guess is that you will find the best price through some travel agency and not directly from any particular airline, especially for a fairly indirect routing. You will also find that, as a budget traveler, you have fairly little say on your routing or itinerary.
Meanwhile, I doubt NW would offer very good prices from where you are just because you are close to MSP and DTW, both dominated by NW. The travel agencies I mentioned will most likely have special deals with Asian airlines, usually Korean, EVA Air (Taiwan), China Airlines (Taiwan), Asiana (S. Korean). Both Korean and China have poorer than average safety record, I believe you have been informed by now. From personal experience and hearsay, the 4 abovementioned airlines are usually among the cheapest on the transpacific market although Singapore (also Cathay, JAL or ANA, which are normally perceived as costlier options) may surprise with special low fares during off-peak seasons. Again it will ultimately depend on which agency you purchase your tickets from, while the various posts here on this forum can only give you a list of possibilities.