In fact, there is a quick and easy way of this kind of GC-related timeouts, which does not depend on the complex collection and configuration of data, and this will work every time you work on Linux.
As noted elsewhere, whether timeout recessions caused by your Newgen, CMS or FullGC expectations are acceptable depends on your requirements. It's also true that setting up GC HotSpot mechanisms is a complex art, and you usually need a lot more detail and iterative experimentation to figure out how to improve your current behavior.
However, if you want all these pauses and associated timeouts to disappear without getting a PhD in the GC setup, there is a simple hack way: the Zing JVM will run this 32GB Solr heap with the GC, never breaking a sweat, and without any associated with GC pauses, crashes, or related timeouts. And he will do it out of the box, with default settings and virtually no configuration.
And yes, I work in Azul and am proud of it. We save people with such difficult weeks of effort and tons if the embarrassment of a timeout all the time.