Well, I could not find a way, so I indeed applied for a Brazilian visa and flew in, as flights in and out of Brazil are a requirement to obtain the visa.
Still, to put this question to rest, I finally dug out the information which was not that hard to find once I took a few lessons in Brazilian Portugese. The official site of the Brazil government even includes a snippet in English answering exactly this question:
Take note that the Brazilian visa will never be granted in Brazilian
territory. Therefore, it is not possible to obtain your visa in
airports, ports of entry or any other point of the Brazilian border.
It might have been different a while ago but this is the information published as of today January 10, 2017.
Credit:stackoverflow.com‘
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