A citizen from another South American country may well be able to cross at certain border entry points without too much difficulty, however us gringos who stick out like a sore thumb aren't quite that fortunate. You will most certainly be required to produce a passport and visa no matter where, when and how you try to enter Brazil. On top of that little problem, even if you were magically able to enter by some twist of fate if you were caught, under the present circumstances of having already been "invited" to leave the country voluntarily, you would most certainly be detained again and this time they wouldn't make it a request - they'd just start a deportation process. If you know the Federal Police here then you know only too well that they don't take kindly to people trying to jerk them around or put one over on them.
You can't do ANYTHING here in Brazil unless you are in a "regular" migratory situation. Without being within your valid visa stay, you virtually can't sign in to use a public toilet - REALLY. So, if you're "irregular" you can't do anything that requires you do deal with a Cartório or civil laws, much less enter the permanency process. If you haven't already noticed Brazil is really big on documents. You are required by law to carry your identifying documents and at the very least a certified copy of your passport ID page and visa pages with you at all times in order to prove that you are "regular". It is a police state, if a police officer requests you produce your identification you are required to do so, without any exception, othewise you are detained until you are identified. For example, if you're in a bar and a fight breaks out, the police will ID everybody in the bar and not just those participating in the brawl. At that point it's game over for anybody here who doesn't produce ID or is "irregular".
Trust me, if there was ANY other way for you to come back into the country before waiting out your time I would have told you so. The only options you have are to wait or try to obtain some other category of visa. There really is no use in trying to invent different scenarios to slip past the Feds, it just won't work. If you don't want to listen to my advise that's up to you, but please I can only tell you what I have already told you and this is becoming rather tiresome.
Cheers,
William James Woodward, Brazil & Canada Expert, Expat-blog Team