We've made great progress since then, and he now lets me put the saddle on without much fuss, though I still have to move slow. However, he is still nervous and presses himself into the wall if I saddle him up in his stall. He is also nervous of blankets. He is not blanketed regularly, and it took me a good 15 minutes to get a cooler on him. He is fine once the blanket/object is actually on his back, he seems to not like the very act of putting it on. He even gets mildly nervous if someone hands me a jacket while I am riding.
The section I bolded is part of your problem.
In the wild, what moves slow? A predator sneaking up on prey. This is what your horse thinks of when you sloooooowly try to lay a blanket on his back.
In general, it sounds like you need to take a step back and properly desensitize your horse with ground work.
Timing is also key. If you release pressure too soon, he learns nothing. If you release pressure too late, he'll wig out.
Present your saddle blanket (or any object) to your horse. The very instant he shows signs of nervousness (wide eyes, wide nostrils, raise head, etc), you need to STOP bringing it closer. Immediately. Then hold steady. Do not remove the saddle blanket until you see some sort of relaxation from him (licking lips, blinking, lower head, etc). Then immediately turn away from him and take the blanket away.
For the first time, you may need to stop 10 feet from him, if he shows signs of nervousness then. Do what you need to do.
If he moves his feet (you should never do this when he's tied up), go ahead and let him move. But do not bring the blanket closer, nor let it move farther away. Keep your distance exactly the same until his feet stop moving (sign of relaxation). Then immeidately remove it.
Repeat. Repeat. Repeat. On both sides. Work on this every single day.
Approach and retreat.
You are trying to teach your horse that when they relax in a stressful situation (or stop moving), they get rewarded by having the stressful object taken away. This is why if you take the object away too soon, they will learn that "freaking out" make the object go away. Or if you remove the object too late, they will learn that relaxing did NOT make it go away. Timing is important.
And don't try to sneak the blanket (or whatever object) closer. Be loud and proud about it. I intentionally am loud and all over the place when I desensitize. So they learn that me waving my arms about, jumping, and whatever, makes no difference and is nothing to get excited about.
I very much doubt he has such great fear because someone plopped a saddle on his back one time. He just needs more ground work and desensitizing work. He needs to know he can trust his handler. Right now, he doesn't.