I would first check so see if he is sore in any places where the saddle goes. Sometimes that can cause a horse to become girthy. Push with your hand around his wither area & along his back & watch his reaction.
If he doesn't have any soreness issues, try this: When you go to tighten the saddle, bring a crop with you. Hold the crop downward in your right hand & proceed to tighten the saddle. If he nips or kicks, quickly flick the crop into his belly. Eventually he might learn that each time he nips or kicks, your going to nip or kick back.
He should learn this quickly & the nipping & kicking will stop because he's too afraid to get smacked again. (Trust me... this will not hurt the horse... he's 1000 pounds of muscle.)
I have used this method on a old mare of mine who was always girthy (She had no soreness issues.). Now she has never nipped or kicked me... just puts her ears back a little... as long as she doesn't threaten to hurt me that's ok.
He seems like he is a pushy horse... heres a technique I use: Go buy a long crop, training stick, dressage whip, or something that is a good extension of your arm. Fix your horse up in the halter & lead, grab your whip, & go for a long walk. During your walk, stop your horse. Say whoa & stop in your tracks. If he doesnt stop with you, add halter pressure. Next, reach your arm out with the whip & imagine drawing a huge circle around you the distance of your arm & whip together. That is YOUR bubble. Your horse should not be in that space. If he is, push him out of it. Don't use the halter, use the whip. With rhythm, smack his chest until he moves out of your bubble. If he is not responding increase the pressure of the smacks every four hits until he moves back. Keep repeating: Walk, stop, back him out of your bubble (If he is in it) & repeat. Eventually, when you stop he should stop immediatly with you & out of your personal space. Some horses take to this pretty fast. If you make this a regular thing to work on, he'll learn to always stay out of your space. Make sure you reward him by YOU walking into HIS space & giving him a pat on the forehead.
Make sure you really pay attention to rewarding him & YOU moving into his space so that he learns he doesn't always have to move away from you as you get closer.
Consistancy & Patience.