It's going to come out when it's ready. I use a shedding blade in the spring. I use it until my arm feels like it's going to fall off. Then I do it again the next day, then the next, then the next. Eventually all the winter coat will be gone.
This is ten minutes of using the shedding blade. It looked like my horse had exploded on the grass. Lol
As far as I know there are no quick fixes. You can clip the horse, I guess but I don't do that.
I have recently started grooming Halter horses for a retired Judge.
He has me take a small black rubber curry -he orders them special so they are extra hard, as the ones you typically find have a lot of flex. I use short, FIRM strokes with the grain of the hair. Each horse takes me around 20 mins and I work them 5 days a week. (Took longer when I first started, but is better when you keep up with it - and the day after their day off takes me a few mins longer still)
For the show conditioning:
After they are curried, I apply a glycerin mixture to their neck and shoulders and put their neoprene sweats on. They are lunged at a fast, long trot in our large round pen for 10 mins in each direction. They are then place in their stall for 30 mins to an hour while their "saunas" work on breaking down fat cells.
We have recently started to keep light nylon sheets on them since it is starting to cool off at night.
They are not under lights yet.
Short of giving them a full body clip, there really is no method to strip a horse of his winter coat in a couple of days. Horses (like all animals) don't shed all their hair at once, it comes out in layers. So you can brush them until they don't have any remaining loose hairs one day, and the next day a whole new set will be ready to loosen up.
Baths can often help speed up the process a bit, as well as the tips you've already heard for speeding it up.
Warm water. Giving a warm bath isnt always best in chilly temperatures unless you have a heated barn or stall you can put them in afterwards. Warm water loosens any animals coat up and makes it easier to get out the loose hair.