Hi Selpol
Welcome to the wonderful world of RTW planning, one of my favourite pastimes
I assume you are thinking of a business class ticket (based on the ticket you priced up being ~$6500)

Some comments:

HEL-YUL stopover on Finnair
...first will be Oslo, Helsinki, Toronto...
If you want to go to Toronto (YYZ) why are you flying to Montreal (YUL)?
Finnair does not fly to either airport currently, so you are changing planes somewhere (It commences HEL-YYZ non-stop flights on May 4th)
(I plugged your itinerary into the tool, and it offered flights via London)

DFW-GRU stopover on AA
GRU-DFW
...planning to visit Buenos Aires and possibly Asuncion...
Again, if you want to go to Buenos Aires, why are you flying to Sao Paolo?
AA used to fly direct DFW-EZE, but you can easily fly DFW-MIA-EZE (and of course stopover in Maimi if you want to), also DFW-JFK-EZE
As an aside, if you travelling between Buenos Aires and Asuncion, you really must visit the Iguassu Falls
As a further aside, I have no idea how the winter weather is down there in August

KUL-OSL on QR will of course by via DOH
So your current itinerary is: OSL-HEL-xLHR-YUL-DFW-GRU-DFW-TYO-HKG-KUL-xDOH-OSL
You could stopover in either London or Doha but not both (maximum of two stopovers in your continent of origin, and you're already stopping over in Helsinki)

Your itinerary is only using 11 of the allowed 16 segments
Can't leave 5 segments on the table, right?
One way to use them-
- assuming you are based in the Dallas area
- lots of AA non-stop flights from DFW
- to Anchorage, Vancouver, Calgary, even Quebec City
- to Mexico and Central America
- to the Caribbean
- and to all over the lower 48 states
So
- a return trip over the Memorial Day weekend (ie after Europe and before Sth America)
- another return trip over the Labor Day weekend (ie after Sth America and before Asia)
- and finally, a stopover in Honolulu on your way to Japan,
Something like: OSL-HEL-LHR-YYZ-DFW-ANC-DFW-GRU-DFW-AUA-DFW-HNL-TYO-HKG-KUL-DOH-OSL

The above itinerary exceeds the 34,000 miles allowed on a business class Global Explorer, but it is a valid 4-continent Oneworld Explorer, and starting from Norway they are the same price.

Happy planning Selpol