But yeah, in the interest of not getting involved in spaghetti posting and keeping my thoughts understandable, here is a write-up on why I think the Rotholz approach is the best plan for him. I am not saying it will win him the battle, our position is strong. But it is a much better option for him than just a central charge, in my opinion.
How Von Trotha can try to win the battle
Ok, so lets look at the map of our position. We have a very strong central position, with three artillery batteries dominating the center. An infantry assault in the center is not likely to work, since our infantry is superior to his and our artillery can shoot at short-medium range during a defensive battle. Thus, if he is to win, he must use his artillery to soften up our position. In order to do that, he presumably must screen them with infantry and cavalry, without exposing said infantry and cavalry to too much damage from our guns. Fortunately for him, there is hilly terrain both East and West of our position, providing cover within which his army can maneuver, without taking fire from our guns. In all other parts of the map, all his units will slowly but surely take damage from our cannons, putting them on a timer. Within this "safe" area, marked in green, he has all the time in the world to maneuver, move up his artillery and Rest his units.
View: https://imgur.com/a/G7UweZq
Thus, I propose he will advance through the Rotholz, attempting to push us out of the Eeastern hills and taking up positions with his infantry and horse artillery as shown below. In this position, his horse artillery can fire on the hills, so he would have a good chance of taking them and forcing our infantry to retreat.
View: https://imgur.com/a/2BreVqq
Note that his infantry is completely safe from our central artillery here. They can Rest, while he slowly moves up his artillery. At this point, we will not be able to see what he is doing behind the hills. Our options will be to wait for whatever 10+ turns it will take him to maneuver, or to leave our entrenched position and get into a battle at the hills, where our artillery cannot fire and his can. After he completes moving his artillery up, he can try to setup something like this:
View: https://imgur.com/a/o6qTV1W
Red arrows are cavalry ready charges. Circles are artillery.
In this position, his artillery can get to work, bombarding and with good rolls, destroying our position. Of course, the obvious thing we can do is to charge his non-screened artillery with our cavalry. However, this is an obvious move, that he is sure to expect. Thus, he has all the cavalry Ready Charge, and all infantry Ready Fire. Consequently, any of our cavalry that enters the same hex as his artillery is likely to die, the cavalry charge would be a suicide mission. And unless we destroy all his guns in our charge, we are left with no cavalry, meaning he can use his cavalry freely to flank us, go after our artillery and potentially win. Also, if he Ready Fires his artillery, expecting our charge, the cavalry will take 6 short-range artillery shots on their way in, in addition to the Ready Charges from his cav. The charge might very well fail, and then we outright lose.
In essence, I consider him forcing us to charge his artillery to be a win for him, since it forces us out of our turtling strategy and gives him the potential to win the battle. Sure, influence-wise losing 4 units of artillery for 4 units of our cavalry is terrible, but he does not want to maximise his influence, he wants to win the battle and defeat us.
As a final note, do I consider this approach from him likely to work? Not really, a lot of things would have to go right for him and wrong for us for him to win. But I do consider this approach to be one that gives him a real chance of victory, and one that allows him to use his strong artillery and generally defensive setup efficiently against our current position.