I'd start by using a 3rd party booking engine (e.g. Orbitz, Expedia, etc) and seeing what they come up with as options for price and routing that involves CO. If they have something and it really is an S fare then you'll need to book at co.com if you want the 100% EQMs. Here's where things get "fun."

Get the specific list of flights - both CO and non-CO - and go over to co.com. Book the trip as though it is just the CO segments (HKG-GRR or NRT-GRR, whichever you find from the booking site). When you get to the end choose to pay by Western Union rather than with a credit card. Don't worry about the price being all wrong. This will give you a PNR for that itinerary. Then you have to call the co.com support desk and give them the PNR and the additional segments that you want added in. They will "fix" the reservation to add the other carriers' flights in and reprice things. At that point it should be the same price as shown on the 3rd party site and you can complete the booking and get your 100% EQMs.

Be careful on which partners you use. As of October 25th CO is out of SkyTeam so those partners get no credit. And while it is assumed that *A partners will start to earn credit at that point it hasn't been announced officially.

There is also a decent chance that you will not find the S fare as the inventory might not be available; you may have to pay more for the trip based on that, at which point the co.com booking issues may just disappear.