I like your post, and I think you have received nice suggestions here. I think that giving your teen his space is the best you can do in first place. After that, being there when he wants/needs to talk will encourage him to spend more time with you. It is not going to be a huge amount of time, but it will build a bridge between you both, and that is exactly what you want.
Without nagging and pushing too much, I ask my 16 year-old teenager help with the yard or garage cleaning, and while there we talk, we laugh, and he opens himself in such a casual way that we both enjoy our time together.
When something happens, and he is in a bad mood, or sad or upset, I do not ask anything until he feels calmer, and then I say to him, "remember I am here to listen if you need to talk".
When he needs, we go together to buy new clothes for him. Once a week, we go and have a hamburger and fries together (I don't eat hamburgers, I order a veggie sandwich, lol), I let him talk, and that really is an open door to his world. I do not criticize his friends, or actions if I do not like them or I do not agree with something, I make suggestions sometimes, in a friendly way, something that may help to open his mind and look to another direction depending on the matter.
I think things with teenagers should go smoothly; however, you do not need to be their best friend, and allow what is not allowable. Show him you are always there as a parent who listens, and as a parent who has rules and boundaries, but with love and respect.
It is easy? nope, parenting is not easy, but we can do a lot while the kids are still at home.
Let him know you love him, and you are proud of him when he is "a good kid", and let him know, calmly and firmly, when he is wrong or when things are not going in the right direction.
We may not be able to "maximize" our time together with our teens, but we are able to "maximize" our quality time together with our children.