I know what you mean about wanting an amazing bond with a horse...But I've also had experience with finding an amazing bond with a much older (15-20 year old) horse.
He was one of the horses at my camp, a little POA, and when he came to camp for the first time he was just scared to death but afraid to show it. I basically took him under my wing (since my fellow horse counselor people were terrified of him) and coaxed him out of his shell.
He wasn't push-button at all either. He must have been somebodies show pony or something because he'd do dressage, all on his own and he was always collected. He was also extremely flighty, terrified and very sensitive to everything. He always came through in a crisis though!
I rode him everyday, every time we rode anywhere, and didn't ride any other hoses unless I was forced. I adored him, he adored me. The second summer, last summer, he came back to camp and I was a horse counselor again. He neighed when he saw me, after a year apart.
It's so amazing to have a horse want to be with you so bad that when you walk away he watches after you and ignores everything else until you come back.
I was going to buy him instead of adopting Lacy but he developed some health issues that I really didn't want to have to watch him suffer, then eventually die from and on top of that I really was too big for him since he was a smaller POA.
BUT, I just want to let you know that an older horse can bond with you like you've never seen before and an older horse can teach you so much too. I'd advise you to get an older horse, find one that you absolutely adore and get a foal somewhere farther down the road.
Sorry for how long this is...