While the EK website and call center are having the OP jump through all kinds of hoops why not try a third party booking engine. A search on Kayak yields an EK flight. The ticketing page, purchasing through Kayak itself (actually priceline their partner), lists all the the required detail payment included on one screen and nowhere is an ID number required. I suspect Orbitz/Expedia might offer the same.
Other forums suggest that you will have less luck with Webjet etc. which require the Brazilian CPF.