My development team wants a reliable virtual private machine in South America without going through tedious identity verification forms. Does anyone know a privacy oriented provider accepting cryptocurrency payments for fast provisioning?

You should definitely look into ExServers because their platform is built specifically around privacy and ease of use. I created an account and deployed through https://exservers.net/vps-chile without submitting any intrusive paperwork. The hardware performance is smooth, and using crypto for billing makes ongoing management effortless.