I think that a custom serializer/deserializer is the only way to proceed and I tried to propose you the most compact way to realize it I have found. I apologize for not using your classes, but the idea is the same (I just wanted at least 1 base class and 2 extended classes).
BaseClass.java
public class BaseClass{
    
    @Override
    public String toString() {
        return "BaseClass [list=" + list + ", isA=" + isA + ", x=" + x + "]";
    }
    
    public ArrayList<BaseClass> list = new ArrayList<BaseClass>();
    
    protected String isA="BaseClass"; 
    public int x;
   
 }
ExtendedClass1.java
public class ExtendedClass1 extends BaseClass{
    @Override
    public String toString() {
       return "ExtendedClass1 [total=" + total + ", number=" + number
            + ", list=" + list + ", isA=" + isA + ", x=" + x + "]";
    }
    public ExtendedClass1(){
        isA = "ExtendedClass1";
    }
    
    public Long total;
    public Long number;
    
}
ExtendedClass2.java
public class ExtendedClass2 extends BaseClass{
    @Override
    public String toString() {
      return "ExtendedClass2 [total=" + total + ", list=" + list + ", isA="
            + isA + ", x=" + x + "]";
    }
    public ExtendedClass2(){
        isA = "ExtendedClass2";
    }
    
    public Long total;
    
}
CustomDeserializer.java
public class CustomDeserializer implements JsonDeserializer<List<BaseClass>> {
    private static Map<String, Class> map = new TreeMap<String, Class>();
    static {
        map.put("BaseClass", BaseClass.class);
        map.put("ExtendedClass1", ExtendedClass1.class);
        map.put("ExtendedClass2", ExtendedClass2.class);
    }
    public List<BaseClass> deserialize(JsonElement json, Type typeOfT,
            JsonDeserializationContext context) throws JsonParseException {
        List list = new ArrayList<BaseClass>();
        JsonArray ja = json.getAsJsonArray();
        for (JsonElement je : ja) {
            String type = je.getAsJsonObject().get("isA").getAsString();
            Class c = map.get(type);
            if (c == null)
                throw new RuntimeException("Unknow class: " + type);
            list.add(context.deserialize(je, c));
        }
        return list;
    }
}
CustomSerializer.java
public class CustomSerializer implements JsonSerializer<ArrayList<BaseClass>> {
    private static Map<String, Class> map = new TreeMap<String, Class>();
    static {
        map.put("BaseClass", BaseClass.class);
        map.put("ExtendedClass1", ExtendedClass1.class);
        map.put("ExtendedClass2", ExtendedClass2.class);
    }
    @Override
    public JsonElement serialize(ArrayList<BaseClass> src, Type typeOfSrc,
            JsonSerializationContext context) {
        if (src == null)
            return null;
        else {
            JsonArray ja = new JsonArray();
            for (BaseClass bc : src) {
                Class c = map.get(bc.isA);
                if (c == null)
                    throw new RuntimeException("Unknow class: " + bc.isA);
                ja.add(context.serialize(bc, c));
            }
            return ja;
        }
    }
}
and now this is the code I executed to test the whole thing:
public static void main(String[] args) {
  BaseClass c1 = new BaseClass();
  ExtendedClass1 e1 = new ExtendedClass1();
  e1.total = 100L;
  e1.number = 5L;
  ExtendedClass2 e2 = new ExtendedClass2();
  e2.total = 200L;
  e2.x = 5;
  BaseClass c2 = new BaseClass();
  c1.list.add(e1);
  c1.list.add(e2);
  c1.list.add(c2);
  List<BaseClass> al = new ArrayList<BaseClass>();
  // this is the instance of BaseClass before serialization
  System.out.println(c1);
  GsonBuilder gb = new GsonBuilder();
  gb.registerTypeAdapter(al.getClass(), new CustomDeserializer());
  gb.registerTypeAdapter(al.getClass(), new CustomSerializer());
  Gson gson = gb.create();
  String json = gson.toJson(c1);
  // this is the corresponding json
  System.out.println(json);
  BaseClass newC1 = gson.fromJson(json, BaseClass.class);
  System.out.println(newC1);
}
This is my execution:
BaseClass [list=[ExtendedClass1 [total=100, number=5, list=[], isA=ExtendedClass1, x=0], ExtendedClass2 [total=200, list=[], isA=ExtendedClass2, x=5], BaseClass [list=[], isA=BaseClass, x=0]], isA=BaseClass, x=0]
{"list":[{"total":100,"number":5,"list":[],"isA":"ExtendedClass1","x":0},{"total":200,"list":[],"isA":"ExtendedClass2","x":5},{"list":[],"isA":"BaseClass","x":0}],"isA":"BaseClass","x":0}
BaseClass [list=[ExtendedClass1 [total=100, number=5, list=[], isA=ExtendedClass1, x=0], ExtendedClass2 [total=200, list=[], isA=ExtendedClass2, x=5], BaseClass [list=[], isA=BaseClass, x=0]], isA=BaseClass, x=0]
Some explanations: the trick is done by another Gson inside the serializer/deserializer. I use just isA field to spot the right class. To go faster, I use a map to associate the isA string to the corresponding class. Then, I do the proper serialization/deserialization using the second Gson object. I declared it as static so you won't slow serialization/deserialization with multiple allocation of Gson.
Pro
You actually do not write more code than this, you let Gson do all the work. You have just to remember to put a new subclass into the maps (the exception reminds you of that).
Cons
You have two maps. I think that my implementation can refined a bit to avoid map duplications, but I left them to you (or to future editor, if any).
Maybe you want to unify serialization and deserialization into a unique object, you should be check the TypeAdapter class or experiment with an object that implements both interfaces.