no import paper for the bike
yes, Foz is maybe the best for you, I had a similar problem in 2003. In the morning many bikes cross to bridge between Brazil and Paraguay, most people going to work, so I just joined them and rode out of Brazil over the bridge only stoping in Paraguay. Of course the immigration in Paraguay asked me for the exit stamp from Brazil, as I did not get one. So I walked back over to Brazil, got my exit stamp and walked back into Paraguay. In Paraguay I went to the customs and got an import paper for the bike.
The police in Brazil has no idea about the import paper, so dont worry about them.
In Santa Elena (going to Venezuela) I had also to leave Brazil without bike papers, because coming from Guyana they did not want to let me with the bike into Brazil, saying that I would need a letter from the embassy in Gorgetown. Also Santa Elena was easy, I just rode past the customs, nobody stopped me.
But my advise is, keep your paper work in order in Brazil otherwise you can get in big trouble.
Greetings from Bulgaria