How do I increase the task response timeout window?
This timeout is actually hardcoded into the runtime, as below:

In Android, application responsiveness is monitored by the Activity Manager and Window Manager system services. Android will display the ANR dialog for a particular application when it detects one of the following conditions:


No response to an input event (such as key press or screen touch events) within 5 seconds.
A BroadcastReceiver hasn't finished executing within 10 seconds.


This is relevant to apps themselves, but Chrome (or whatever browser you are using) can also be affected as above.

For further information refer to the Android Developer's Guide: Maintaining Application Responsiveness.