To use the pre-cut shelves, I realized a mistake I made above. If you used the 12" shelves for sides inside the 16" front and back, the ext. depth would be 13 1/2", comparing apples to apples. This extra 1/2" almost makes up the decreased volume caused by using 3/4" instead of 1/2". I calculated the internal volume of your plan, using 5/8" as 7,756 cu. in. (53.86 cu.ft.). If you used the 3/4"mdf, with the 13 1/2" depth, the internal volume would be 7,743 cu.in. (53.77cu.ft.)-practically the same.

Internal dimensions would be 14 1/2 x 44 1/2 x 12, so there shouldn't be a standing wave problem, huh?