Sum of the values in nested dicts excluding some based on other key in MongoDB database

Question

I have a MongoDB database with the following format:

    {
    "_id": xxx,
    "timestamp": "1643649900000",
    "scores":
        [{
        "name": "APPL",
        "price": 80
        },
        {
        "name": "GOOGL",
        "price": 83,
        },
        {
        "name": "COMPI",
        "price": 76,
        },
        {
        "name": "and more names which also can change in the following documents",
        "price": 76,
        }]
    },
    {
    "_id": yyy,
    "time": "1644350400000",
    "scores":
        [{
        "name": "STCMP",
        "price": 33
        },
        {
        "name": "APPL",
        "price": 95,
        },
        {
        "name": "GOOGL",
        "price": 83,
        },
        {
        "name": "MINN",
        "price": 76,
        }]
    },

I need to sum all prices per time but excluding (or subtract from the sum) some.

My scores list has around 200 dicts and I want to exclude around 5 of them. I only managed to do the summing part, but after two days of search still can't manage to exclude with my limited knowledge.

toBeExcluded = ["APPL", "GOOGL"]

sums.aggregate([
            {
                "$unwind" : "$scores"
            },
            {
                "$group": {
                    "_id": "$time",
                    "total": {
                        "$sum": "$scores.price"
                    }
                }
            },
            {
                "$addFields":{
                    "timeAdj": {"$toInt": [{"$subtract":[{"$divide": ["$_id", 1000]}, 300]}]}
                }
            },
            {
                "$sort": {"timeAdj":1}
            }
            ]))