Elasticsearch: alternative to cross_fields with fuzziness - elasticsearch

Question

I have an elasticsearch index with the standard analyzer. I would like to perfom search queries containing multiple words, e.g. human anatomy. This search should be performed across several fields:
Title
Subject
Description
All the words in the query should be present in any of the fields (e.g. 'human' in title and 'anatomy' in description, etc.). If not all the words are present across these fields, the result shouldn't be returned.
Now, more importantly, I want to get fuzzy matches (for example, these queries should return approximately the same results as human anatomy:
human anatom
human anatomic
humanic anatomic
etc.
So fuzziness should apply to every word in the query.
As Elasticsearch doesn't support fuzziness for the multi-match cross-fields queries, I have been trying to achieve the desired behaviour this way:
{
"query": {
"bool" : {
"must": [
{
"query": {
"bool":
{
"should": [
{
"match": {
"title": {
"query": "human",
"fuzziness": 2,
}
}
},
{
"match": {
"description": {
"query": "human",
"fuzziness": 2,
}
}
},
{
"match": {
"subject": {
"query": "human",
"fuzziness": 2,
}
}
},
]
}
}
},
{
"query": {
"bool":
{
"should": [
{
"match": {
"title": {
"query": "anatomy",
"fuzziness": 2,
}
}
},
{
"match": {
"description": {
"query": "anatomy",
"fuzziness": 2,
}
}
},
{
"match": {
"subject": {
"query": "anatomy",
"fuzziness": 2,
}
}
},
]
}
}
},
]
}
}
}
The idea behind this code is the following: find the results where
either of the fields contains human (with 2-letter edit distance, e.g.: humane, humon, humanic, etc.)
and
either of the fields contains anatomy (with 2-letter edit distance, e.g.: anatom, anatomic, etc.).
Unfortunately, this code does not work and fails to retrieve a great number of relevant results. For example (the edit distance between each of the words in the two queries <= 2):
human anatomic – 0 results
humans anatomy – 21 results
How can I make fuzziness work within the given conditions? Recreating the index with n-gram is currently not an option, so I would like to make fuzziness work.