It's not crazy at all, and well worth a short experiment using the online tool. Price a DONE4 ex-ARN using the online tool, and be sure to click on the "taxes and fees" item on the pricing screen (and print it) to see the fuel surcharge numbers ("YQ" on the breakout.)

Then price a DONE5 ex-USA with AA as the first, hence ticketing airline, and do the same thing. It might be close to a wash; who knows.

You'd obviously need to vary your itinerary because of the first and last legs (from/to USA) to something like LAX-xLHR-EBB//JNB-WDH//VFA-JNB-SYD-CNS-SYD-SCL-IPC-SCL-LIM-EZE-JFK-SFO or some such.

One benefit of the US origin would be your ability to seriously accelerate your status and mileage earning potential by signing up for the Platinum Challenge (see the AA board) through which you gain Platinum status if you earn 10,000 elite qualifying points on AA-numbered flights within 3 months. Once you get to Plat, miles earned in some (not all) other Oneworld airlines' flights earn an elite bonus of 100% redeemable miles, which really adds up quickly. You don't earn Plat bonuses on BA-numbered flights, or JAL or Malev ones, but you'd get it on all the Qantas and Lan flights in your itinerary, also Iberia.

Business class flights on any Oneworld flight earn 1.5 elite points per mile, so for example LAX-LHR on AA is 5456 miles, hence earns 8100+ points.

Now here's where it gets interesting. If you don't stop over (24h +) in the UK, you can book the LHR-EBB flight using an AA flight number (BA plane) thus the 4000+ miles on LHR-EBB (6000+ points) added to the LAX flight gets you well over the 10,000 point limit right away.

Seat-of-the-pants calculation on the above revised itinerary looks like you'd earn around 90K redeemable miles if you take the Plat Challenge; whereas you'd earn around 54K miles if you don't. And your route is far from optimized for mileage purposes, if that's an interest.

Also if you don't stop over at LHR and use the AA codeshare, you won't be charged for the premium-cabin UK air passenger duty, which for LHR-EBB in business would be £100.

Note I used LAX as your origin point since you'd have to fly on AA transatlantic to get the AA mileage/points, and AA doesn't have a nonstop flight to London from SFO. Starting in SFO would require you to use an additional segment to get out of the USA (e.g. SFO-ORD-LHR) and you want to preserve segments.

Maybe you could fly on your own dime (but use AA metal for the points) to ORD or JFK and have the RTW ticket start there. LAX-LHR on AA appears to arrive at LHR after the EBB flight has left, so you might encounter some resistance to being able to use the AA code on the next day's EBB flight, since you'd be spending the night at LHR. You'd have to have the AA code in order to make the 10K points for the Challenge. Originating at some other AA gateway (ORD, DFW, JFK, BOS...) you can get to Heathrow early enough in the morning to make the EBB flight.

Sorry, it gets more complicated, but do give it a try as an experiment with the online tool.