I would try to install his "whoa button" while working on the lead line first and once he has "whoa" on the lead, then move toward lunging. Just walk with him leading him as usual and give your "whoa" command. Give lots of praise when you get a response. Once you have it consistently, give him a little more lead and room and repeat the process. The better he gets, the further away you can let the lead/lunge line out until he his finally lunging.
Also practice "whoa" EVERYWHERE. Walking out of the stall, whoa. Walking to the paddock, whoa. "Whoa" randomly and often with lots of praise. Some people don't like to treat their minis, but I do and I would in this instance in order to establish a solid reward. I would not treat often, but once in a while to reinforce the positive behavior.
Once the walk/whoa on the lunge is solid then work on the trot/whoa.
One thing that helps me when they trot and don't want to come down or stop is to lower my energy and breathe out, then stop moving my feet (I tend to walk small circles as I lunge) and step backward drawing the horse towards me, facing me, if possible. Sometimes this will break up their momentum and get their thought back on what is being asked.
Hope this helps a little. I had a Morgan who was just like you mini, loved to trot on the lunge. I used to get dizzy
until we came to an agreement.