Well since the score should be inversely proportional to the position, I was just thinking something like this:
"script":{
"source":"if (<condition on doc>) { return someFunction(_score) } else { return null }",
"lang":"painless"
},
SomeFunction could be something simple like 1/_score, or maybe something more sophisticated. This should give you the relative positioning of all documents that fullfill your condition. However, you obviously wouldn't have the exact position and would lose all information about the "position distance" between the documents.
In addition, the exact _score values obviously will not between consistent at all between different searches. If you need any of that, then I'm afraid I'm out of ideas for you.