I agree that being overly forceful is not a great idea, especially for a beginner, who cannot always know how to be firm without being "mad". And, I agree to try a new tactic if the first one fails. This experience, while frustrating, is going to expand you abilities as you work to find a solution. And although it isn't really safe, it isnt like the horse is going all bronco on you the instant you hit the saddle.
First of all, don't keep trying to bring the stool to the horse. That allows the horse a "rest" and starts the whole process from ground zero all over again.
Always bring the horse to the stool. Always., even if it means repositioning THE HORSE again and again.
If he starts to move reprimand him instantly. Don't wait until he has already moved off and you are in the process of chasing him. Give him a sharp "Ah! Ah!" the instant you see him start to even think about moving. You'll see him shift his weight and start to lift a foot. NoW!
If he still moves , give a little snap to the reins . He KNOWS he is supposed to stand there. He is taking you for a ride. You let him know that you will have none of it, and be quick and firm, and when he gives up that thought, don't stand around petting him , just a short , calm , good boy, and get on.