Thanks for all the advice, guys!

The itinerary is technically 16 flights, and I was planning on using other flights to explore more of each content. I'd figured that using their tool would guarantee that the flights were actually possible and since I'd thought it was a flat rate anyway, I thought I'd go all out on my first try. I also assumed that I'd be able to somehow find at least connecting flights to/from each pair...Does the 16 flights mean that flights with one layover count as 2 flights, and 2 layovers count as 3, etc?

So I'm guessing I should focus on keeping the itinerary to larger airports then. Honestly, not too interested in Europe/North America/China, so that takes away a lot of the bigger airports, but I'll give it another shot and see how it goes. Thanks all.