Sounds like you are making progress.
FWIW, here is what I’ve been taught for de-spooking a horse, and it works. In a situation like this one where the fear object is an animal that is mobile, modify as needed. I’d probably do this with the fear-object-animal in a pen, to start with.
Bring the horse as close to the fear object as possible where he is still rational and rideable (or, from the ground, responds to the handler’s directions). Don’t get into the geographic panic zone, because no creature can learn while in panic/adrenaline state. In the rational zone, but in sight of the fear object, put the horse to work, under saddle or on the ground. Work work work, just the usual work, not frantic work and not into a lather, horse should not be distressed, just working. Keep going with no pauses. Ground: longeing or even just leading back and forth, turning, backing, etc. Under saddle: no walk, mostly trot, circles & figure eights, some canter, trot-canter transitions, etc.
After a few minutes of work, give the horse a pause and a rest as close to the fear object as they are still calm. While they are standing resting and becoming more calm as their heart rate and breathing settle down, extravagantly praise and reward them for calmness. Petting, rubbing behind the saddle, kind words, lavish it on them and make this the best moment of their day.
Rinse & repeat during each de-spook session. Several minutes of work-work-work followed by two-three minutes of rest as close to the fear object as they can be calm, with praise-praise-praise. Quit the session before their brain is too tired to respond well, maybe 15-20 minutes.
The idea is to create a situation where the horse associates the fear object with rest, praise, comfort and relaxation. Only expose the horse to the fear object during these sessions until they show they are no longer spooky about it. That is, don’t allow an uncontrolled encounter where the horse refreshes its fear.
This technique not only works, it works fairly quickly. Twenty minutes of alternately work-work-work then rest near the fear object can create a remarkable level of change. Several sessions of this can de-spook a horse from even a terrifying fear object.
It may take more than one session to thoroughly and reliably de-spook a particular object. And if the fear is very deeply ingrained it may need to be repeated from time to time throughout the horse’s life.
This technique works a charm if it is done with awareness and sensitivity.
Like any other technique, the best results are if it is used consistently. Every time the horse spooks at anything. Not just when it’s convenient for the rider. Even if it feels that training progress on a spooky horse is being de-railed by constant de-spooking, in the long run de-spooking promotes less distraction, and therefore better learning. And a less spooky horse can matter the most when more advanced training and performance is asked. Everything is better on a calmer, less spooky, more focused horse! 
As practiced over time of course – De-spooking more than one object with this technique, basically de-spooking everything the horse spooks at, can gradually create an anticipation in the horse that he’ll always be asked to be calm if he spooks. It helps teach him to calm himself. He may still spook at something new, but at a lower level of intensity. As soon as the work-work-work starts he’s fairly prompt to respond well to the rest phase. Over time the horse gets less spooky generally because their expectations and state of mind are changing.
The first time I ever tried this technique was with a horse that literally dragged me when I wouldn’t let go of the lead rope while he was fleeing in panic from some large white lawn chairs. I wish I had a video of that, but I don’t know how to selfie video while being dragged by a panicking horse. So, once I had the situation in hand again, I went straight to this de-spook technique. It wasn’t easy at first as the horse was so alarmed at any glimpse of those white plastic chairs. But 2 sessions and 3 days later, I did get video of him walking calmly up to the chairs, grabbing them in his teeth and chewing on them. He volunteered the grabbing and chewing of the plastic chairs he couldn’t even look at a few days previous. That was years ago, I’ll see if I can find the video.