A lot of my work involves designing and building climbing walls, so I have to do a lot of research and testing on screws as these are the things that hold many climbing walls up. For all our timber construction we use KTX screws from Concept Distribution in Blackburn. We have pull tested these screws on a test jig, both in shear, and for a straight out pull, and I am constantly amazed by how strong they are. Our weapon of choice is normally the 5x50 KTX interior screw which we merrily apply 350kg loads to on the test rig when screwed into 18mm birch plywood, and we've never had one fail.
Over the years we have tried all sorts of screws, but these appear to be the most reliable and by far the strongest.
My advice is to always put plenty of screws in, balance the screw placements in the faceplate so they are evenly positioned, and make sure they are done up tightly enough so the wood is pulled tightly onto the face plate, but don't go too heavy handed otherwise you'll start to wind the screw thread through the wood and weaken the fixing.
The story of screw chucks breaking is a little un-nerving, but I guess you only have one fixing so its doing a lot of work. Plenty of screws on a face plate seems like a better plan!