I think you can get griddata to approximate the spherical topology by replicating some of your scattered input points before calling it. Try duplicating all the points in the longitude interval [0 30], for example, and add 360 to the longitudes of the duplicates. Then duplicate the points in [330 360] and subtract 360 from the longitudes of the duplicates. Now your data set will span, roughly, [-30 390]. Grid it this way, then truncate both east and west to bring the grid back to [0 360].
Then, before calling contourm, use georasterref to set up a geographic raster reference object, R, and use the contourm(Z,R,...) syntax. As long as R.Lonlim spans 360 degrees, contourm will handle the longitude wrapping from here. (Don't try to use the contourm(lat, lon, Z, ...) syntax.)
