5/8" MDF is often a special-order item. Chances are you won't be able to find it at a big DIY store; I've certainly never been successful. Find a full-service lumber yard and ask them to order what you need. Or call custom kitchen cabinet makers in your area and ask them where they buy plywood and other sheet materials. The place I use caters to cabinet makers, so they have just about everything in stock. Anything they don't have, they can get in 2-4 days.
If you can't find what you need, you might be able to go with slightly thinner wood and a slightly thicker acrylic overlay.