The small pump will provide enough vacuum to do average size cores just fine provided it is being done correctly. The best way I have come up with to bag wings is to add 1/4" pressboard to the outside surface of the shucks. Sand the corners of the pressboard so there are no sharp edges that can puncture the bag. Then place 2mil painters tarp between the shuck and the wing sheeting. For adhesive I always use laminating epoxy resin. Once the core has the sheeting in place and they are in the shucks place the shucks into the bag. Then put 3 layers of paper towel on the top shuck/pressboard to act as a breather. The breather is important to get a consistent pull over the entire surface. Make sure you are working on a flat surface and that the vacuum port is more of less centered. Seal the bag and pull vacuum.