The error you mentioned seems to be related to permission issues.
Are you the product admin for Analytics? If not please make sure you have the access of product profile in which the report suite and its variables like evar, props(which you are trying to use in API) are added in the permission section of the product profile. You can ask one of system admin to check it for you under admin console.
UPDATE: It looks like I was setting body not correctly; I thought I would be able to get data for all the 3 dimensions associated to a metrics with one request, while it looks like you can get data for only one dimension associated at a time.