Adam is usually more likely to overfit, so using SGD with Nesterov momentum might help a bit. I'd also recommend augmenting contrast, brightness, saturation and hue if those options are available for the ImageDataGenerator class.

Also does the rotation in the ImageDataGenerator fill the background with black pixels or is there the option to extend/reflect the image? In my experience simply filling the background with black after rotation tends to hinder the accuracy.

One trick that might also help is to extract the outputs not only from the last layer of the pretrained network but also from earlier layers to feed into your network. In my experience this can help improve the accuracy. I've done this with the EfficientNet B0, so I've pasted some example code here to help you out, though if you don't want to use an EfficientNet I'm sure this can be adapted to the DenseNet201 too.

Of course, sometimes transfer learning just doesn't help really, so if nothing else helps you push the accuracy above 90% it might be best to just build and train your own model from scratch to better suit your needs.