As promised, reporting back now that
my RTW is (finally) successfully ticketed. This is my first, and I can't emphasize enough how essential FT was to making this – and my now-upcoming yearlong vacation – a reality. Thanks to all the experts here who are so generous with their knowledge!
The short version: After a few phone calls and a lot of messages with their Twitter support team, Qantas successfully ticketed my ex-JNB LONE5 for only a little more $ than the online tool (which errored out every time) indicated it should be.
The long version:
- First Attempt - Call with QF (30 min) - Agent said they had no way to book any RTW if the website didn't work, and that if there was an error at payment it meant the itinerary was invalid in some way.

- Second Attempt - Call with AA RTW Desk (15 min) - Agent said it was impossible for AA to ticket any RTW without an over-ocean marketed by AA.

- Third Attempt - Call with QF (3 hours) - Got lucky and got an agent who was willing to try hard to make it work. We spent the first hour walking through my full itinerary in the online tool to "prove" that it was a payment-related error, not an invalid itinerary. Spent the second hour mostly on hold while she manually constructed that itinerary in a different system. And then spent the third hour in a game of telephone between me, her, and the rate desk as they claimed a number of new reasons my itinerary wasn't valid (detailed below). Call ended when I asked the primary agent to allow me to speak to the rate desk agent - I was transferred and while introducing myself she hung up on me.

- Royal Jordanian isn't a Oneworld carrier.

- You can't start and end in different parts of Africa. (pointed out the exception in the rules)
- You can only start/end in different parts of Africa if you also have an intra-Africa segment as part of your overall itinerary.

- The website says "additional terms and conditions may apply" so we can say no to whatever we want.

- Mauritius is an island so it's not actually part of Africa (or any other continent).

- "I looked at a map with my supervisor and Mauritius is clearly not part of Africa."

- You can only book to Mauritius using a travel agent, it's impossible for us.
- Fourth Attempt - Call with QF (2 hours) - Called back immediately and somehow was lucky enough to get an agent who knew the agent I just spent 3 hours on the phone with and was willing to find out from her where my itinerary was temporarily saved. She tried one more time with the rate desk - who again told her Mauritius wasn't part of Africa - and then I gave up and had her take my payment with LHR-JNB as the final segment instead of LGW-MRU.

- Success! - Messages with Qantas Twitter Support - At this point I wrote a direct message to QF's Twitter support succinctly detailing the above and asking for help. They took over my reservation and over the next 24 hours figured out that I was correct it was valid and promised they'd figure out how to ticket the itinerary with MRU in it. It took a full week from first message to receiving my ticketing confirmation, but was so much less painful than any more calls.
The final price (3080 USD including taxes/fees) was a little higher than expected from the online tool (2954 USD including taxes/fees) but oh well. I was curious and figured out the price difference was mainly due to an additional YQ charge of $120 - couldn't figure out which flight that came from.
If I had this to do over again I think I would have simply gotten a QF agent to the point where the itinerary was input manually into their system & had a record locator and then switched to Twitter messages for the full pricing/questions back and forth. When I need to change dates for the second-half of my RTW I'll try just messaging them the changes I want.
One other note I hadn't seen posted here, so sharing in case it's not well-known: While you can only select seats for LA flights on LATAM.com - not JJ flights - you can select seats for your JJ flights on the RJ website.