Do as the drawing shows but with taller brackets.

If you make the taller, also make them wider. I'd make up some cardboard examples and see what looks good onsite full-sized. Couple hours of effort for lasting results you like.

I assume the designer selected a 6" x 24" x 24" that is a standard manufactured size readally available from a building supply source. Check standard sizes unless you are willing to pay custom prices.

Here's poly examples. They can be stacked. Craftsman Brackets (wholesalemillwork.com)

Thank you to those that replied. I’ll likely go forward with brackets after all.