What are alternatives to MLP, when you have rectangular, structured data?
Fancy deep learning architectures mostly work by exploiting structure in your data. Permutation invariance or equivariance, temporal structure and spatial structure come to mind. Maybe some features are based on a set of the same objects? Most of the benefits come from sharing weights and learning a shared representation. Another potential benefit is the flexibility in output, although that is less relevant in your case. If you have a lot more labeled data on another task with the same features, you could pretrain a larger model on that task and then fine tune that network on your current task. For the rest it is difficult to say without showing some examples.