It looks like there's plenty of beef in the legs on the corners. If you get brass screws that are large enough diameter and long enough, they shouldn't pull out. Be sure to pre-drill the holes the size if the screw shanks (so the shank is snug on the hole and only the threads bight into the wood) and lubricate the hole with some paraffin, soap, WD40, whatever so the screw turns fairly easily going in - you don't want to bugger up the screw heads on such a good looking piece of work. If you use WD40 or any liquid, be sure it doesn't spill out of the hole at all or it will soak out behind the finish and stain your wood. I would drive the screws by hand (at least the last few turns) just to be safe. Alternatively, you can use a chrome opener and attach with stainless screws.
Nice job on the finish
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Scott, Portland, OR '85 V-20 I/O, Merc 170