I agree with the sentiment others have posted. If you've resolved to pay for a positioning flight anyway, I think you'd be better off originating the RTW in the middle of the itinerary and paying the much cheaper non-US price.

For example, while the LONE4 from the US costs, $5300, a DONE4 from AMM is $7200. If you're not using all 16 segments anyway, the AMM-DXB segment would be free to tack on and start your actual vacation from there.

For $1900, getting every flight in J, 100% EQM, and 150% EQP is a pretty darn good value. That SYD-LAX (13 hours!) segment alone commands a $2000-$3000 premium in J over Y even in the most-discounted J (I) that's sometimes available.

You'd also have a bunch of extra North America segments to play with that book into domestic F to run up miles. Some BOS-DFW-SEA-DFW-BOS, BOS-ORD-SFO-ORD-BOS, etc are good times for mileage runs when F is guaranteed...