I'd suggest not writing off the gulf coast. Though you may have visited a beach over there that was largely made of shells or crushed shells that isn't the only type of gulf beach that you can find. We like the beaches at the Fort De Soto county park (to the south of St. Petersburg) with its nice sandy beach and warm gulf coastal water. While it may be an element of the time of the year that you've visited, we've found that the Atlantic coast weather at the beaches feature much colder, windy temperatures than on the gulf side.
As for the oil spill, I understand that the concern had been for the Key West area and (though I think it's counter-intuitive) the Atlantic side beaches. Based on what some of my Florida friends say none of those concerns have been realized - at least so far.
Despite all of that, we like Cocoa Beach, too - just a different beach experience with the rougher wave action, colder water, and the touristy town of Cocoa Beach (and I don't mean any of that in a negative way). And, while we haven't visited them, there are beaches - like Melbourne Beach - that stretch to the south of Cocoa Beach just off route A1A that might be less touristy.
Cocoa Beach is about an hour east of the general Disney area via state route 528. Fort De Soto park is about two hours (I-4, I-275, state route 679/Pinellas Bayway South).
Dick Taylor