For n=6, this doesn't seem to be an issue, since strlen(superpermutation) < 1000. URL's can comfortably increase towards 2k characters in most setups. Apache defaults to 8k I think, don't know about PHP.
When the search moves to n=7, we'll enter the 6k range of lenght of superpermutations. This might not cause any issues, but I wouldn't bet on it.
It might be better to use POST to send the document across to the server.