I'm wowwed like your correspondents over on contextearth and am greatly looking forward to some statistician somewhere checking it out so you can get version 2 of the paper published :). I can't see too much else you can do.
I found this [site](https://sites.google.com/site/medievalwarmperiod/Home/historic-el-nino-events) for evidence from historical documents going back to 1500. Everybody has selection bias but I doubt that historical researchers have been trying to justify some 4.3 year number.
I stripped out the data [here]( https://db.tt/LFXDYjCR) but haven't thought through how to compare it with your results - there weren't any going back that far last week. if you get what I mean.
Anyway, this continues to be a very educational, steep learning curve and a really enjoyable project.