Pat, you might want to check with the Iate Clube do Rio de Janeiro (ICRJ) to see if they have a reciprocity agreement.
Iate Clube do Rio de Janeiro
You might get 3 days that way. The problem here is that the number of yachts (especially big motor yachts) is growing so rapidly that marinas and clubs can't keep up with the demand. Problems of a booming economy and too much money!
I still think it will be hard to stay in Rio on a boat during the olympics, but nothing is impossible. If you want to avoid the tourist hotel thing there is also the possibility of a homestay in Rio or renting an apartment on a weekly basis. There is (and will be) a shortage of hotel rooms in Rio so these have become common solutions to the problem. Renting an apartment will let you entertain as you mentioned you'd like to do. But do charter in Angra before or after. You'll love it. It will be winter and the days are not too hot and the weather is generally sunny, dry and very pleasant. Both Ilha Grande and Paraty are well worth the visit.
Se precisar de alguma coisa, Ú sˇ falar. Abrašo!