Firstly, thanks for implementing the dynamic number of luggage carts based on payload :-)
GSX is great but still more time-consuming than it needs to be. And, faster is more realistic.
1) Make the baggage handlers throw suitcases faster. That belt should have at least 3-4 bags on it at once. Surely they aren't ALL lazy unionized workers.
2) Have an "initial prep" option that will have the ground crew just install the nose gear pin and connect the tug. That can happen at any time, including during boarding, and will save time when initiating the actual pushback.