If your requests need more than 30s, something is wrong. Most apps strive for <200ms responses. If you need a long time, rearchitect it. Run a background thread. Poll for completion or email the user when complete. Again, annoying, but your app will be better for it.

Saying that a legacy product sucks, but that you still need it to run is not an effective mindset. These platforms have constraints. Work within them and the app will scale and perform very well.