Make sure you're in Rio for New Year's Eve (Reveillon) which is a definite "must do" for a couple of days at then of the trip. The main problem will be getting reasonable accommodation as many hotels put up prices or have min. stay packages. Unfortunately NYE is on a Sat. night this year which is when two of the more accessible samba schools, Salgueiro and Mangueira, have their rehearsal. Do try and get to a rehearsal by one of the other schools. One day will be taken up with Sugar Loaf and Corcovado. As an fan of arquitetcure you'll probably want to visit the museum by Oscar Niemeyer in Niteroi. This will take up at least half a day from Copa/Ipanema

IMO the other "must do" in Brasil is Iguaçu Falls but you'll need to 2.0-2.5 days to get there and back plus sightseeing to do it justice.

I can see the attraction of Brasilia but a day and a half should be sufficient. It would be helpful if the award ticket got you to Brasilia at the start of the Brazil portion. BTW, the historical cities around Belo Horizonte are relatively close to Brasilia with the works of the Aleijadinho and may be of interest.

I think Manaus would be too far unless you really need to see just the theatre and nothing else (which would seem a waste).

In short I would do .
Brasilia 1.5 days
Iguaçu Falls 2.5 day
Rio 3 days

Any more is too crammed an itinerary IMO. If your more interest in arquitecture heavily outweighs your interest in natural wonders substitute Iguaçu Falls for BH/Manaus.

Finally, depending on your schedule Gol www.voegol.com.br may be cheaper than a Varig/Tam pass but GOL is a LCC and thus stingy with baggage allowances.