Instead of clearing the glass you may want to make the beach a tourism destination for the world’s many ‘beach glass hunters’. I was at Cheung Chau last year and we had a wonderfultime collecting beautifully smooth beach glass and pottery fragments. These ‘glass beaches’ are very popular … search for Fort Bragg in California, Hawaii’s beaches, and others where glass accumulated from rubbish (a glass barbecue area in your case by the sound of it) … then the sea tumbles it to create ‘treasure’. Sharp glass is no fun for walkers and kids, but if the glass you refer to is tumbled sea glass, think of promoting the beach as a wonderful outing for beach glass hunters like me 
It was a magic afternoon I’ll never forget.