I'm sorry, but your current ideas sound like bullshit managerial metaphors to try and trick your underlings into caring.
Building tower from bricks
This one reeks of a thin veneer of false incentive. A physical reminder of the work ahead and behind. I understand the theory. It's supposed to make it fun and give people a physical thing to take pride in. But I have never seen such a ploy work. At best it comes off as "yeah, that's Bob's thing, he likes to see how we're doing". At worst the reinforces the cynical ones to feel like they're being treated as stupid children. Even as as child I could see through this sort of bullshit.
Climbing on some hypothetical everest, where each camp is release stage
As depicted as what? A chart with a mountain in the background? Same sort of managment fluff as the brick tower. If you want to make your motivational powerpoint slides more cute, sure, go for it. But "cute" doesn't get code out the door.
Some badges system, like StackExchange system
Now, this one I had to contemplate. At SE, I come here of my own free will and participate because I care. ie, I'm already motivated. The bronze badges are mostly bullshit incentivators to go try out all the different aspects of SE. The 'nice answer' and 'good answer' badges I actually do kind of care about. Because those are a judgement of my peers. Nameless, faceless peers that melt into the masses in a way that is completely unlike a small development team. You could try an anonymous employee of the month submission.
But if you want to gameify code releases, you should actually incentive your coders. I wouldn't particularly hand out money. See RSA motivate. No, if the team makes a goal, give them a reward. Real rewards. From wearing jeans, free pizza, extra time off, an Xbox in the lounge, choosing their next project, or actual money. Let them all submit reward proposals and vote on what they want. Veto what you will and then organize a tiered reward system which makes meeting and beating deadlines a game with actual rewards. Without real rewards, gamification only works on the gullible and easily deceived.