This won't help people currently in the process of getting a visa, but it might help a small group of people in the future...

Each time I was at the Brazilian consulate here in Santiago to get my visa I met other US citizens who told me that they intentionally leave the US to get the visa in another country, being sure that it's a country whose citizens are not required to have a visa - like Chile - so there's usually no backlog.

Speaking with other US citizens when I was in Rio solidified this - I was amazed by the number of people who travel just to get their visa. Of course, you need to have the time and funds to get to another country, spend a week while the visa is processed, etc., but apparently it's quite a popular option. It has it's own pitfalls, too, but I thought I'd mention it.