In MongoDB, how do I update by matching an element within an array of an Embedded query?

Question

Say you have an document saved like this:

{ 
    _id: "1",
    thingy: {
         moreStuff: [
             {
                 _id:"a",
                 moreComplicated: [
                     {
                         _id:"a1",
                         info: "test"
                     },
                     ... // More similar elements
                 ]
             },
             ... // More similar elements
         ]
    }
}

Suppose you already have a way to get the query of the document:

db.getCollection("thingies").find({"_id": 1});

Now you're looking for a way to update the "info" section inside the "a1" object nested within all those other objects and arrays. The only catch to this is that "moreStuff" and "moreComplicated" arrays are being updated constantly, so aiming by array location (like thingy.morestuff.0.moreComplicated.0.info) won't work. The only way to do it is by looking up the unique mongoID of each object.

How would you query the arrays by matching an element to value instead of an index? Bonus points if you can have a "find" query return a similar object.