I have a QGIS (2.10.1) project that contains several shapefiles, all of which are EPSG:3338 (NAD83 / Alaska Albers). The project property CRS is also EPSG:3338. All of the shapefiles display correctly, and the project is to my liking.
However, when I subsequently add a basemap via the Web > OpenLayers plugin, the project properties are immediately forced to EPSG:3857 (WGS 84 / Pseudo Mercator), and the map display changes accordingly.
I do not want the map to display in Pseudo Mercator. How do I maintain the project's original NAD83 / Alaska Albers CRS while displaying an OpenLayers basemap?
Note that the project's "on the fly CRS transformation" setting has no effect. Regardless of its initial setting, it always will be checked on after adding a basemap.