1. Hex heads can be covered with custom made 'caps', so can cap "screws" - just need rod stock and a lathe, etc. Others: truss head, button heads, etc.
2. Most 300 series SS (and 18-8 grade) 'fasteners' are now made in asia .... and who the hell knows what their strength and chemical composition is ... unless accompanied by 'certifications'.
3. You can get 'slotted' round head ... just need a perfectly fitting & bodaceous screwdriver to 'set them'
4. 300 series stainless is still OK ... just remember that without significant additional crevice corrosion that it will take ~ 1 million load cycles at 30 ksi ... about one circumnavigation.
5. Crevice corrosion is attenuated by mirror polishing, .... electro polishing after mirror polishing is even better
6. What you have are anchor head or 'carriage bolts' ... good for horse drawn carriages, farm equipment and little else ... simply because they fit into a 'square hole'. The bolt's OK, the concern is what it does to the mating part .... weakens it due fatigue enhancement.
7. Increase the plate thickness.

Next time you see 'rust blooms' on structural stainless .... investigate, investigate, .... and then usually replace.