Spokane is nice, but you probably mean GIG.

With that itinerary you're going to have a lot of C flights. There simply isn't as much F coverage in the S. Pacific (NZ doesn't have it) or S. America (JJ does but not a ton of availability). Based on this it might make sense to only redeem in C. I'm not sure it is worth it to pay 60K extra point just for one or two flights in F over C. Actually, I'm sure that I wouldn't having made a similar mistake back when CO considered BF "F" for SkyTeam RTW awards. HUGE mistake on my part.

Also keep in mind that you have to move in the same direction the whole time. So if you start in NAN and your stops are SYD, HYD, JNB, BER, SFO and GIG you cannot do them in that order. You would have to do GIG then SFO.

If you do decide to go for F I'd look for TG flights for SYD-BKK-HYD. You can have up to 23:59 in BKK on the layover if you want an extra city on that deal.

From HYD to S. Africa you can either take SA (I quite enjoyed their Y product; trying C later this summer) or try to route via Europe. Not sure it is worth the extra travel time though it should be a valid routing if you want that and can find F seats.

S. Africa to Berlin will be a tough F seat to find. You'll need to avoid the LH 388 (no awards for partners) but there are a number of other options. Most of them top out in C (MS, TK, SA) but there is LX, too, if you can find the seats. As it is a CO award you can also include VS in the itinerary but that, too, is C.

Germany to S. America has some F seats on LH if you can find them. There's also JJ again but they are a harder seat to find often.

S. America to N. America has AC & CO (max out in C) along with JJ & UA for F options. There's also Copa but probably not worth it if you can avoid it.

Finally, NAN is pretty hard to get to on *A. CO is pulling the HNL/GUM flight later this year leaving the AKL connection as the only option. That's gonna hurt a bit as you stalk NZ long-haul seats (again, C only).