I actually don't see anything in it for you, although if your schedule permits you could include the 4 European segments that are allowed. Ideally you'd like your transpacific on Cathay, but that eats another segment HKG-NRT. In your shoes, I think I'd actually pay for the HKG-SIN-HKG separately - it's short enough to not pay for more than coach, and probably won't break the budget. Then ORD-LAX-HKG-NRT-HKG (HKG-SIN-HKG) HKG-NRT-LHR-(europe)-ORD. You can of course buy a 5th segment in Asia for USD150 in coach, but some airlines insist that "extra" segments be chronologically after the included segments, and HKG-NRT is too long to languish in coach, and $300 for D class doesn't seem much of a value.

Remember that when you get home you will have 4 North American segments to use as you see fit, until the one-year expiration, EXCEPT that you turn into a pumpkin when you return to the originating city. So don't begin in ORD, or don't "end" there if you want those segments. You are allowed only 2 stopovers; don't waste one on the way out. You'll burn one when you return home, and that will leave you just one. Have a nice trip ORD-ANC-ORD or something. You can also go someplace and stay less than 24 hours - we did that to SXM once and it worked okay.