Hey bud. Bit of an older post... but you're probably still wondering.
First of all, let's go general. If you're hunting one girl, then a kiss-close is tough. It's make or break, and all your work goes down the tube if you screw it up. However, instead of hunting, take the fishing approach. Pursue 30 girls, and be confident in the fact that you're set no matter what. If this kiss-close doesn't go perfectly, who cares? There are tons of other girls.
This loosens the stress a bit.
Now, for the kiss-close, you've got to work on kino escalation. You were on the right track with the thumb war and hand games... but escalate it. You're keeping it all at the hand level. Build.
My favourite default is massage. Learn how to massage. It's an amazing way to build sexual tension.
Now you just have to improv your way into a massage. Random ideas... she slaps too hard during the game. Mock being hurt by it, and mope. Tell her she's being way too aggressive. Tease her about it. She'll jokingly try to console you.
Don't cave in until she agrees to give you a massage.
You can offer to trade massages, 'if she's good'. When it's your turn to massage, start innocently on the shoulders, then slowly work up the neck to the head. Tugging on the hair a bit will get her excited. Get closer.
This kind of kino, as opposed to the hand slapping, builds sexual tension.
Another playful, innocent way of building sexual tension is to 'sprawl'. Haha. I'm sure there's a better way of wording it... but that's all I can think of at the moment. I do this a ton. It gets the girl laughing, while you get to build the kino.
In your case on the subway, I'd exaggerate a yawn, stretch, and get super comfy. All over her. Kick up your feet, lie down with your head on her lap, rearrange her purse/hands/anything else around you as pillows, etcetera. Act like a cat/dog nestling into its bed. She can't help but finding it amusing, meanwhile you're snuggled up with her. Once you're comfy, and she's at a loss as to what to do with you, just grab her hand and make her pet your head. Get a scalp massage

Again. Keep the situation amusing. With an SPAM like this, you can get away with so much.
This turned into quite the rant... haha. Alright. Lastly, I'll throw some pointers out for the kiss close.
Beforehand, I like to have touched the face a little bit in my kino escalation. Brushing something off her cheek gently, touched her jaw lightly, etcetera. This gets her thinking about the kiss. Gets her wanting it.
When you hug, run your hand into her hair at the back of her head. It's a really erogenous zone for girls... a lot of girls moan when I give it a little tug during a hug. Haha. If you do the 'lean back and gaze into each others' eyes' with your hand playing with her hair... you're sending some pretty strong sexual signals. You can also use that to gently pull her head back towards yours.
By doing that, you eliminate the need to awkwardly lean in for the kiss. You're doing the 'lean in' by just applying a tiny bit of pull. If she's not feeling it, she'll ignore it... but if she's ready, she'll give a bit. That little response on her part is the only permission you need to pull harder, and lean in for a kiss.
I'm hoping you know this, but dead giveaways that she wants a kiss are her eyes flicking to your lips, and her licking her own lips. If you see one or two of these, be confident. She wants it. Do her a favour and take the kiss.
And that's that.
Happy hunting.