If possible can you post your jql query here? If I understand correctly, when you got the one event with an error, it was due to special characters and not the issue. Rather, you are finding that there is a timeout error when you run a search that spans very large result sets. Can you also give a number to this result set? Is it 15,000 100,000 200,000 results, etc.
Additionally, what happens when you specify just the key field (using the fields "key" option) for example -