I found another online syntax tree visualiser that can cope with large trees – phpSyntaxTree. It requires square brackets instead of the lisp s-expression ones, but it should not be too hard to convert from one to another. There is also a Ruby version of the application from a different developer, but it refused to display one of my large sentences that the original had no problems with.
The result of the parse is an image and is fairly easy to read with the leaves (words) laid out in strata (stratas?). My own visualiser is not able to do that at the moment. On the other hand, it uses Graphviz which can output SVG and I am hoping eventually to use that for a semi-interactive tree exploration interface.