I've lost track of how many multi-continents I've flown, but I do at least one per year, some years two, mostly DONEx, but on occasion DCIRxx. I did an ex-US ACIRxx last century, when it was much cheaper.

I'm comfortable with spreadsheets, so I find it very helpful when planning. I can build an itinerary (one segment per row) and see how the connections look in terms of not being too short and not being too long, and play with them (e.g., making a connection an overnight so I can sleep in a hotel), and I can duplicate a sheet and then tweak it. I often have 15-20 versions of an itinerary as I play with different routings, dates, flights. I put the positioning flights and connecting separate itineraries in the same spreadsheet, in different colors. Then, when I'm happy with an itinerary, I copy the flights into my calendar program as events, put the hotel stays in there as events in a different category, and add "enjoyment days" for the full days of enjoying being wherever. That helps me visualize the full thing, with days flying, days enjoying being in a destination, and hotels I'll need to book. When I'm ready to book the trip, I can call the AA RTW desk and read off the flights one by one, or email the itinerary to a travel agent, or try the online tool. You could do much the same just with pencil and paper if you're more comfortable that way. Maybe used lined paper and put one flight or stay in a destination per line.