This will sound counter-intuitive.
I’d practice this at a walk first. Whenever the horse’s barrel swings out against your leg do not let your leg be moved, just tense it up a little bit and hold, then release/relax your leg when the barrel starts swinging away from your lower leg.
I picked up this technique from the wonderful book “The Way to Perfect Horsemanship” by Udo Burger, a book you need to read. Burger explains that when the lower leg is applied exactly at this time it encourages the horse’s hind leg on that side to stay grounded for a split second longer, which results in the horse slowing down.
I do this a lot in my lessons. When I ask the lesson horse to transition downwards from a regular flat footed walk down to a super slow walk I just use my lower legs like this, alternating the lower leg as the horse moves. I have gotten my lesson horse so he will slow down from a free swinging walk down to the super slow walk with this aid only, no hand aids and no seat aids. I use this aid when I want to slow down when I am riding with loose reins.
At the start do this alternating leg aid then, if the horse does not respond at all then back it up with your usual halting rein &/or seat aids. It may take several repetitions before the horse starts to understand it but I usually get the horse to understand it in the first 30 minute lesson I use it in. Accept minor slow downs at first, your seat bone on that side won’t feel as much push from the horse’s hind leg, and that is when you release/relax your lower leg, stiffening up your lower leg on the opposite side because you have to alternate this leg aid for it to work properly. When you get to the speed you want stop using your lower legs unless 1) the horse speeds up again, then repeat this leg aid with reinforcing hand aids if necessary, or 2) the horse slows down too much then your legs start alternating in the more normal way, pressing against the horse’s side as the horse’s barrel moves away from your leg just like you do when you want the horse to lengthen its stride at the walk.
My riding teacher has gotten used to seeing the lesson horse I ride slow down a good bit while my reins are sagging/on the buckle. The horse shortens his stride, his hind legs do not move forward as much, and the horse sort of collects itself even though no rein aids are used. My seat moves back and I start sitting upright because that is what the horse’s back tells me to do.
When your horse understands this leg aid at a walk then you can introduce it at the faster gaits.
It may take a while, but between the cobweb reins and this particular leg aid the often super resistant lesson horses I ride become light in hand and a pleasure to ride.
The book I referred to has been reprinted and is available on Amazon and other sites. EVERY rider should read this book.