If the epi center of the next shaker occurs directly under your home it won't make any difference what you do -- everything is going to come down. However, the kind of preventive maintenance that you've outlined makes nothing but real good sense.
In most situations the "L" brackets will either completely prevent the cabinet from toppling or slow its fall to the extent that persons near by would have a chance to scurry to a safer location (under a doorway opening) without danger of being injured by the falling furniture.
Make sure that the "L" brackets are firmly screwed into the furniture and into the wall studs. We don't think it would be wise to use molly screws or toggle bolts for such a purpose. Make sure that the screw penetrates into the stud at least one and one-half inches. Remember to consider the thickness of the wall covering and or paneling when selecting the proper screw.
If your wall is covered with half-inch drywall you will need at least a two inch long screw. If your wall is plaster you will need at least a two and one-half inch long screw. When installing screws into old dry studs it is wise to pre-drill a small pilot hole first to prevent the screw from splitting the wood. To make the screw easier to install wipe the threads across a wet bar of soap. The wet soap acts as a lubricant for installation, and when it dries it helps to hold the screw in it. And good luck!