Not sure I understand what you're asking. For registration purposes "the bullshit bureaucratic monster called the USA" is utterly irrelevant. What state? Almost any state which allowed you to legally register in the first place has some provision for legally renewing by mail. So what's your problem?
FWIW, no South American country is going to have the means to easily check the validity of your registration. However, they can read an expiration date as easily as you can. And as discussed to the point of absurdity on many other threads, photocopies with shopped-in dates usually pass muster…until they don't.
Hope that's helpful.
Mark
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