Getting arena sour is not nearly as much about what you do in the arena as your timing and what and how you leave.
What I get from your original post is that you ride out of the arena and quit riding somewhere else. You do almost the exact opposite of what I teach people that ride with me to do. When you are done riding, you ride your horse out and go out on the trails and then quit riding. It is my opinion that you are rewarding your horse for leaving the arena.
I usually work and 'drill' horses out in the pasture or on the trail when I can. When I am finished riding, I come back in to the arena, ride around a while and cool the horse out there if he is hot and then quit in the arena. I will ride a horse to the point in the arena farthest from the gate and stand quietly there for at least 5 minutes. Then, I dismount, loosen the girth and lead the horse out of the gate.
If I am working with a barrel racer, I have them walk the pattern, stop at the 3rd barrel, dismount, loosen the girth and lead the horse out -- using a different gate if possible. If their horse is hot, I will always have them cool it out while walking the barrel pattern and will always have them lead the horse out.
If I am working with someone over fences, the horse is cooled off walking around the jumps and again, dismounted at the point farthest from the gate and led out.
If I was working with a roping horse, he would always be ridden into the box, stand for a few minutes and be dismounted there.
Are you getting the point? The arena should be the last place he is ridden. It should be the place that he is walked, rested, cooled out and always dismounted.
Every horse should be anxious to go into the arena and should never dread it as place to only work hard.
When I used to show, as soon as I rode a horse out of the show-pen, I went to a work area and rode the horse a lot harder than I did in the show-ring. I NEVER rode to the barn or the trailer and put the horse up. If you want to make a horse anxious to leave a ring and to dread going into a ring, that is the way to do it.