I guess that maybe your body language is a bit conflicting. It's possible that you are blocking him more than you realize. So, you are asking for forward, but possibly blocking that . Many times people don't realize how conflicting their signals are to a horse. For example, they are saying GO with the whip, but are backing away from the hrose, which is as much as saying "Come here".
If your horse is freezing, then he may be confused.
The other thing is that if he worries about going through a tight space, such as the squeeze you are putting on him between you and the round pen, then that is something that might show up in other situations, such as trailer loading or going through gates and such. Can you work on moving him through squeeze places with him on a long rope, not in the round pen and just at a walk?
OK, if none of this rings true (and remember, I am just specualting since I can't see you and your horse work), then you need to get the hrose to really move out forward . Start by loosening up the squeeze, giving him as much of an "open door" as you can and get him to cut loose and really move out. Do whatever it takes. tie a plastic bag to the whip and make some noise. Get him to stop holding back. And when he goes forward with committment, STOP the whip and let him run.
So, your release is as soon as he goes forward with committment. Do not chase him or try to keep him going. he should feel that the freedom comes in going forward. So, if he comes down, like to a trot, let him, then go and ask for forward again. This works on his responsiveness to upward transitions. you reward the response, not how long he keeps going forward, just that he jumps to it!