There are a few things that are strange with the current model architecture. Usually the embedding size of the intermediate layers is not monotonically decreasing in MLPs. You might consider projecting the input to a larger dimension first (e.g., 1024) and using a shallower network (e.g., just 3-4 layers) to begin with. Additionally, models beyond a certain depth typically have residual connections (e.g., ResNets and Transfomers), so the lack of residual connections may be an issue with so many linear layers.
As for searching for the model architecture, the issue is this usually very expensive, so randomized approaches are preferred over techniques like grid search. A reasonable heuristic with limited computational resources is to start with a much simpler model (e.g., fewer layers, fewer bells and whistles such as dropout) and to grow the model in width or  depth until things stop improving.