I’ll try and answer your questions as best I can, but please bear in mind the Qantas website can be a bit finnicky and just not like some searches for whatever reason.
If you wanted to just try and fix your particular itinerary, if you already know there’s flights available, then you can just try and add each major leg (max 5) until it fails.
For some more general advice: In my opinion, the best way to start searching for award availability, and more specifically business class availability, is to search each major leg individually (i.e. ADL - CMB, or BOG - AMM). You should search for these legs still using the multi-city tool, but only inputting one leg at a time. This will give you a calendar view of when the flights are, and a misleading, but still relevant, view of different class availability. Once you’ve found the flights you want, write them down somewhere, and rinse and repeat. It is a frustrating thing to do, and will take time, but when creating complex itineraries like this it is how it is. I will note though, that Qantas does not let you use certain airports as the first departing port, such as Colombo (atleast on the website).
Secondly, your airline choices seem fine, as they’re all oneworld airlines. You do NOT have to fly Qantas. I will say that Qatar has severly curtailed most of their award availability to Qantas, so you might have trouble finding business class on Qatar.
I think the search is failing due to the lack of the engine to search for flights from DEL - ADL. I punched in your itinerary as follows:
ADL - CMB
CMB - LHR
LHR - SJO
BOG - AMM
AMM - DEL
DEL - SYD
This actually worked, and gave me the correct pricing for a RTW trip (I wasn’t bothered to find biz availability). It does also work to route back to ADL, if you skip the Dehli leg (go AMM - ADL). Someone more intelligent than me can figure that one out. ADL is not a very well connected airport, so you might have better success connecting from the east coast anyway.
Sorry if this creates more questions than answers, but let me know if I can help.