php update nested property in stdClass

Question

I have a stdClass object $patient that is the result of a webservice call. I also have an array of changes $changes that I want to make to that object. But I can't get a reference to the nested properties the way I want. The stdClass looks something like this:

"Patient": {
    "PatientID": 649,
    "PatientClinicalInfo": {
        "Gender": "Male",
    },
    "PatientGeneralInfo": {
        "BillingAddress": {
            "AddressLine1": "123 MAIN ST",
            "AddressLine2": "APT B",
            "City": "SPRINGFIELD",
            "PostalCode": "49024",
            "State": "MI"
        },
        "BillingContactInfo": {
            "EmailAddress": "[email protected]",
            "PhoneNumber": "3185189415"
        },
        "DeliveryAddress": {
            "AddressLine1": "123 MAIN ST",
            "AddressLine2": "APT B",
            "City": "SPRINGFIELD",
            "PostalCode": "49024",
            "State": "Michigan"
        },
        "DeliveryPhone": "3185189415",
        "Name": {
            "First": "Gonna",
            "Last": "Sick",
            "Middle": "B"
        }
    }
}

The array of changes looks something like this:

['delivery_address2' => 'APT 2B', 'primary_phone' => '2695551212']

This is what I was hoping to do (but this code does not work):

private function applyChangesToPatient(array $changes, stdClass $patient): stdClass
{
    $newPatient = $patient;
    $fieldMap = [
        'delivery_address1' => 'PatientGeneralInfo->DeliveryAddress->AddressLine1',
        'delivery_address2' => 'PatientGeneralInfo->DeliveryAddress->AddressLine2',
        'primary_phone'     => 'PatientGeneralInfo->BillingContactInfo->PhoneNumber',
    ];
    foreach ($changes as $key => $value) {
        if (isset($fieldMap[$key])){
            $path = $fieldMap[$key];
            $newPatient->$path = $value;  // This doesn't work!
        }
    }
    return $newPatient;
}

What I've tried

There are lots of tips on stackoverflow for iterating through the object and get the values, that's not what I want.
I've tried lots of different combinations of $$path and ${$path}, but I just can't seem to convert the string 'PatientGeneralInfo->DeliveryAddress->AddressLine1' to an actual reference to that property in the stdClass.

I have tried this, and it works. But I don't like it.

private function applyChangesToPatient(array $changes, stdClass $patient): stdClass
{
    $newPatient = $patient;
    foreach ($changes as $key => $value) {
        switch ($key) {
            case 'delivery_address2':
                $newPatient->PatientGeneralInfo->DeliveryAddress->AddressLine2 = $value;
                break; 
            case 'primary_phone':
                $newPatient->PatientGeneralInfo->BillingContactInfo->PhoneNumber = $value;
                break;
           // etc. etc.
        }
    }
    return $newPatient;
}

I really want to use that $fieldMap array. If that works, I can store the mapping in a separate JSON file and then easily add new mappings when needed -- without the need to change my code!

So, stackoverflow Community? Can you help me?