OP, I say this kindly- I do not think this horse trusts your hands, or your decision making.
In the trial video, you are largely letting him sort things out while you point him around. He’s not finished, but he clearly knows what he’s doing. He seems happy enough to bop along with minimal input from you, relying on his experience.
In the December video, he starts out looking pretty nice, then starts to deteriorate. There are a couple of sketchy distances where he still jumps, but he starts to want to make his own decisions about pace and striding. You start to pull more and he very visibly objects. Then, he runs out. There is a clear pattern here where you are interfering with his way of going, and he is getting frustrated and losing confidence.
In the most recent video, he looks very stressed. I don’t think this is an appropriate time to use a lunge whip to direct him, or to force him over the X- horses just don’t learn in that state of mind. From your description of the lesson, it sounds like he became progressively overwhelmed to the point that he just checked out.
I don’t say this to sound accusatory, or to disparage your riding. You look lovely and balanced, but this horse may have been used to a more experienced or accurate rider, and it can be tough for them to adjust from someone taking care of them, to them needing to take care of the rider a bit. I’m not your trainer and I don’t know your riding well at all, so I’ll refrain from any commentary regarding your trainer or his process, but I would encourage you to consider the poster above who advised getting a second opinion, even if just for a single lesson. I love having fresh eyes whenever I’m dealing with a tricky issue!
Last of all, try not to get discouraged, or hung up on a timeline. I have a number of students who came to me with what they thought were irreparable jumping issues (including two who would not even walk over a pole in hand!) who are now jumping happily and confidently, and the process wasn’t traumatic at all. Yes, it involved going back to basics and putting competitive goals on hold, but now they’re sitting on confident horses, knowing that when they make the inevitable mistake (which most of us do!) they have laid a solid enough foundation that they can carry on after without worry. Life is so much easier when the horse is happy and motivated to work for us.