A common misconception. This is not a RTW award, rather a one world award which allows 35000miles of travel. Travel where you wish.
You can only stop in a city once, you can also transit it though (twice if I recall correctly)
They way you are getting to IAH is going to be the most direct. AA will route you through a hub and don't have domestic J to IAH. If you wanted to save money, you could do CDG-MAD-MIA in J and tack on AA to IAH in Y...but if being in business is worth the extra BA fees for you, then you have the only option I'm aware of. I mean, at the end of the day, it's a business seat... it's going to be good.
If your mileage allows it, I'd be tempted to take the Qatar option. Particulary if you get a decent layover so you can enjoy the Doha lounge. That may be just me though.
Cathay is probably the option back to Adelaide. Otherwise JAL via NRT/SYD and a Qantas flight (if you can get one)... again Qantas charge some solid fees/taxes