Finding documents with "too many fields"

What's the easiest way to find documents from an index that appears to have too many fields.
I want to delete those documents, but there doesn't seem to be a way to easily find them.

The background to how I get here.
The index used to allow up to 2000 fields I believe. So any index created prior to say 7 would have documents containing up to 2000 fields without throwing errors.

But now after upgrade the cluster, new documents with more than 1000 fields would throw errors.
It's not a bad thing to throw errors when there are too many fields. But I can't seem to figure out an easy way to sort documents based on doc_size, or field_size.
We disable scripting by the way.

Any suggestions?

My first reaction was a script might be able to do it, but without that your only option would be to grab all the docs and then do something external to Elasticsearch.