I appreciate your question, but it is not an easy one to answer long distance. I think we are best served if I just outline some basic training principles I use and let you work out possible solutions with your trainer.
Punishment and Reward. The basic principle we use to train horses (and their riders if truth be told). Basically, as trainers, we need to come up with some sort of aid that elicits the response from our horse that we would like, and then reward that response by discontinuing that aid.
“If you are not sure if you got a response from the horse, you probably did not.”
“If you did get the response you wanted, reward that response by relaxing the aid.”
“If you did not get the response you were looking for, you are no longer looking for a response, but instead you are now looking for an over response.”
“After you reward the response by relaxing the aid, ask with a little bit less the next time you ask for the same reaction.”
“The response should not be any response, but instead the appropriate response, or the response that you intended.”
So taking these principles to your issue, as a trainer, I would arrive at using the cluck and the stick. The stick (coupled with the cluck) is a very powerful training aid. The idea is simple: use the cluck simultaneously with the stick behind your leg. In theory, this will teach your horse to respond to the cluck by moving forward. Here’s the trick, if there is any, use the cluck and the stick (behind your leg) at exactly the same time. If you know you got a response, you can relax, reward your horse, and you are done. If you are not sure if you got a response, you did not. If you do not get the response you want, you have have to repeat the exercise with increasing strength until you do get the desired response and you are able to reward the horse by no longer asking him to go forward by using the stick. The only appropriate response is to go forward willingly. If he raises his head, pins his ears, swishes his tail, or kicks out, although these are definitely responses, they are not appropriate responses, so you have to repeat until the response is appropriate—moving forward willingly.
Start this exercise at a gait in which you are comfortable. Often this will be either standing still or at the walk. Once you understand your horse’s reactions to the stick, you can use it in any situation that you need it. Remember that ultimately you want your horse to react by moving forward willingly from using only the cluck. The stick is used only to get him to be responsive to the cluck. The cluck is better because you can use it in the show ring, but more importantly, you can keep both hands on the reins when you are using the cluck which is safer.
If you go back to your basic training principles, enlist the help of your professional, and both of you remain creative with your training, I am sure you can get your horse through this phase. Remember to keep it simple!