Well, you could publish a simple geoprocessing service that uses the Minimum Bounding Geometry tool with either CONVEX_HULL or RECTANGLE_BY_AREA option. Set the Output Coordinate System geoprocessing environment variable to web mercator. This will force the output of the Minimum Bounding Geometry tool to be in web mercator. Your service would return the feature class output by Minimum Bounding Geometry tool.
As far as projecting on the client side, I can't help you. I'm thinking you'll need a service.