Prevent overfitting when decreasing model complexity is not possible
is this about trying to have the model learn the sum function? Because if it is you can always initialize the weights to be 1 and then make the entire model untrainable.
If all weights are one and the model has linear activations it will just compute the sum of your inputs. If its important to you to train the model to do this I would add a Dropout layer (?).

Your model is so simple it can be written down in closed form as it is $\sum_{i=0}^{255*350}w_i x_i$ and therefore I would just set the $w_i$ to be 1.

(In general initializing the weights to 1, the ideal solution, should make training very fast)