Dude, we're like the same person. I was the friendzone mayor throughout my teenage years, and you're waaay ahead of me in having your life on track haha, so if I can overcome it, so can you.
It's not easy to do, and it wasn't a sudden transition by any means. But I managed to stop giving a fuck, and removed the need to apologise, like before if I went for a kiss and got shot down I would actually apologise for it! That's how bad I was.
Become a touchy guy, it should just be the way you are. Baby steps. Here are a few of my pointers that got me started:
1. If she's wearing an interesting scarf or fur collar, touch it and feel it, make conversation.
2. Putting your arm around a girl whilst pointing out something in the distance is less intense and more easily accepted than putting your arm around a girl whilst making eye contact and focusing on her.
3. Pick imaginary things out of her hair. All these are tiny steps but when done a lot, will really get you comfortable with bridging the gap toward escalation. I used to make out like crazy when drunk on a night out, but on dates I SUCKED.
4. "Cold hands, warm heart." This is a routine I like to think I devised, it comes from a saying my Mum and older people in my town use that implies that people with cold hands have a warm heart and warm hands therefore mean a cold heart

Just gently take her hands and say you want to find out if she is coldhearted, it's a bit corny, but it was a huge success for me in becoming more touchy feely and there is a lot of room for flirting and making her laugh.
5. Kissing shouldn't be done during the big "is he going to kiss me?!" moment like at the end of the date, be playful. A girl asked me to go and get some rizlas for her as I was going to the shop and I said "Only if I get a kiss" and that was our first kiss and start of a relationship.
6. The biggest thing is being a physical leader. It took me SO long to get the courage to do this, but if I meet a girl off the train I will offer my arm or even grab hers and link it with mine and I will take her hand to lead her somewhere etc.