Will, I did see this response in another post.
No - larger screws will interfere with the rotation of the traveller cleat.
You can offset the base slightly - about 1/2" and drill new holes for the rivet / screws. Be careful not to drill the screw holes too large. When you screw them in, turn them like a tap - 1/2 turn forward, 1/4 turn back, repeat. That'll help "cut" the threads into the aluminum extrusion.
This could provide an easy solution. Whatever is done I recommend applying a little Lanocote where the stainless steel screws and rivet contact the aluminum crossbar. Lanacote is an excellent product used to reduce galvanic corrosion between the dissimilar metals. Do not use an aluminum rivet when reattaching the base plate. Aluminum will rip right off. Monel is preffered but West Marine sells stainless rivets that work great.