I am trying to create a world map, but centered over the Pacific rather than the Prime Meridian. Recentering the projection (standard Mercator) on 180 degrees gives me a lot of ugly artifacts where countries are stretched across the "cut line" of the map.

I assume I need to do some kind of intentional clipping (like clipping to hemisphere with an orthographic projection), but I'm not sure how properly to make QGIS cut everything cleanly on a meridian. Is there a standard way of doing this? A plugin?

(I am using the Natural Earth 50m countries shapefile.)