Doing this as a MR? Or primarily to visit these destinations?

You might want to post this question instead in the respective forums here for oneworld, SkyTeam, or Star Alliance if it's the latter - there's a lot of threads about planning RTW trips using the alliances' RTW products. Especially so in the oneworld forum about their xONE products. If you're looking to earn AA or CX miles that might be the place to ask this.

Typically those types of fares have to be booked directly on the phone with one of the alliance member airlines, or on the phone/in person with a travel agent. However the alliance's own websites have downloadable and/or online tools for planning out and validating RTW itineraries.

I haven't done one yet, but I've played with some RTW itinerary ideas using both the Star Alliance and the oneworld calculators. Unfortunately I had to go back to work