In Ecuador we bought the SOAT insurance for one month costing $3.00. we were stopped at least 10 times by police at various check points who wanted to see documents,not once were we asked for insurance.
In Columbia we were stopped at check points, they wanted to see all papers, including insurance. ( the purchase of insurance was required when we imported our bikes from panama to Cartagena Colombia)
Wether you can use the Peruvian SOAT or not, I can not tell you this. We found the When entering Ecuador, we were not required to purchase the Ecuador SOAT insurance but did out of choice as it is so cheap. In Columbia, purchasing the Columbian SOAT was part of the importation process of the motorcycles.