We did haltering and restraining on the first day and days with Cadence... Restraining in a hug and not letting go, for a minute or two, and maneuvering the foal around by applying pressure to the chest or rump to move forward and back. After a few days, we added pressure to the halter to encourage movement, but not enforcement on the halter alone until the foal was several weeks. Always the foal was asked to go forward with the halter and then given pressure onbehind with either hands or a soft butt rope.
Did you/have you done the method of making the 'foal suitcase' with a long line?
I have, and it works great. I may not be doing it the same way you do, but I'll bet it's similar. I take my 25ft soft cotton long line and slip the end through the noseband of the halter, then down between the front legs, then up and over the withers and back down to be snapped to itself. This way, when you pull on the lead, you're not putting any real pressure on the halter, it's all around the girth area. If I need to, I can take the excess lead on the other end and loop it behind to use as a butt rope. I'll take a picture of it this afternoon and post it tomorrow.